Though you cannot just keep inviting friends and others to join your group. This will cause Facebook to impose a ban on you. Try following the below mentioned steps -
Choose a Perfect Name
If you want to go popular, you need to have proper name. Don't just give a name straightaway. Come up with a few ideas, make a list, edit them and discuss with friends/ family for suggestions. Look for similar groups on Facebook and check what works for them.
Motivate your friends to invite their friends
Ask your existing friends to join your group. Encourage them to invite their friends to join. Since the Facebook friends typically share the same interests, it should be a great idea to increase the number of members. But take care not to be nagging. Requesting once or twice must be enough.
Publish content that can go popular
Posting content that has the potential of going viral is one of the most important needs. Keep track of current Internet and social networking trends and present a good content on it. Make sure to make it share-able.
As a final point, though, I would remind you that there is nothing like overnight success. Facebook gives an opportunity to grow your groups gradually. Don't just rush.
Live....and Let Live!