I am facing problem with google Chrome browser

From the screenshot you have provided, it does not appear as if there is any issue with your Chrome installation. I would guess the message appears as a result of your anti virus preventing the secure transaction because your connection is not secure. The error message does not mean the browser has any issue and it is not stating that the site is insecure. Your message states that the connection is not secure.
I am on the latest version 57.0.2987.110 and I can launch any secure sites easily on my Chrome installation.
There are a few ways with which you may be able to resolve the issues.

Fix Date and time

• Right click on the Clock on your task bar.
• Choose Adjust Date/Time
• Click on Internet Time
• Click on Change Settings. Check the box that says Synchronize with an Internet time server.
• Choose a server and then click on Update.

Clear Browsing data
Cleaning browser data on your Chrome installation can solve the problems sometimes. You can attempt to sort out the issue by clearing the cache.

Turn off SSL in your Antivirus
You can turn off the SSL or HTTPS scanning in your anti-virus software. The setting for the same should be available under the tab that deals with anti fishing settings.

In most cases, it has been observed that the clock settings are the major culprits. Hopefully, the fixes described above should solve your issues.

This is not a browser issue but Admin / Authorize issue which can be enabled or disabled from SSL / https option either from the computer (firewall) setting or Anti-virus (if you have installed it). You have to disable the SSL / https option to visit the required webpages which the browser can't verify the SSL encrypted data to the server visited from your browser or from anywhere else.

Try the above author given guideline to proceed. If it still doesn't work then try the following.

Try to to disable https / SSL from the system by proceeding on 'Proceed' from advanced' option from the error page. Try to bypass the error message in Chrome with just two simple clicks and move on providing the website you are visiting is completely 'secured' one.

Now try to clear the cookies or browser history to browse successfully without any issue.

Thank you so much, to both experts for your valuable suggestion. My clock is already is sync with window server, so it cannot be an issue. It was Avast which was creating the problem. There was an option in its settings "Enable https scan." It was turned on. I just turned it off, and everything starts working.
However, I still wonder why Avast was creating the issue with that option. It can scan https, and it should show them as secure if they are.

Chrome is labeling the non HTTPS websites as insecure since Sept. 2016. And now any site that does collect data through session information is supposed to use HTTPS SSL. In your case thee website is from Google which has it's security certificate for HTTPS is not read by the chrome, so it marked gmail as unsafe. And it is not allowing to go on the login page.

Considering google itself issues the HTTPS SSL certificate to it's google sites users and blogger users. You can guess that Chrome not recognizing the HTTPS SSL certificate that forces the secure condition. This can be solved simply by resetting your connection through modem or router. This way if the connection reset checks the new call for the HTTPS call from your browser through ISP to google server. If this error happens to other sites which has expired SSL then that error will reflect. As this error reads clearly that it failed to check for Gmail's HTTPS verification.

1. You can disable the HTTPS in google chrome.
2. Reload the browser till it forces the HTTPS connection.

You can read the solution here : https://support.google.com/chrome/answer/95572?hl=en

This problem has nothing to do with the antivirus, browser cleaning, clock syncing etc. This is SSL certificate problem which is going to be applicable for every browser after 2018. Chrome being proactive started forcing the sites with authentication to use the HTTPS and not allowing the users to go on such pages.

After January 31st of this year, the 56th version of the Chrome web browser got released. the users are going to find a significant change in the browser in the way it will display the websites that are not having HTTPS, which are also known as SSL.
This latest release of Chrome 56 would reach you with your latest update wherein, any website which is not running as HTTPS would display a message saying "Not Secure" on especially those pages that collect passwords or banking details like credit or debit cards and more. At times even Gmail could even show the same message.

Google has given a technical description on how to implement the SSL certificate on the websites. You can follow those steps and find a solution henceforth.
Even I faced the same issues with many sites, including Gmail, after making these necessary changes, things got resolved.

This might be the problem of SSL connection error. Chrome has made some changes in security level. Due to this many of us are facing various issues with this browser. Recently, I have also faced some issues with Chrome. Frequently, my Gmail account getting logged out. It is all because of this security reasons. I will give some reasons and suggestions for this issue.

Reason for the Error
1. There is no up to date certification.
2. There is an un-trusted certificate issue.
3. There is a possibility of issuing unauthorized authority certificate.
4. The web page contains both secure and nonsecure items.
5. Mismatch of date and time in the local system.
6. There might be a background scanning process by Antivirus for encrypted connections.

Solution to solve the Error
1. Right-click on the Google Chrome shortcut icon.
2. Go to properties option.
3. Select the shortcut tab.
4. Find the target option in the list.
5. Modify the option with "-ignore-certificate-errors-" at the end of the extension.
6. Click Apply and OK option.