Why you want to increase google plus followers? why don't you try to increase members for google community  or google+ page?
I found a thread on the forum mentioned to your question
Check it out 
https://www.webmastersun.com/threads/12568-How-increase-google-plus-group-followers
Hope it helps!
		
 
		
	 
That's this very thread!! LOL
	
		
	
	
		
		
			Anyone know how to increase google plus group followers?
		
		
	 
Yes. Thanks. 
Oh you want to know how to actually do that too. Sorry my bad.
I presume you actually mean 
Google Groups? Because there is no such thing as 
Google Plus Groups.
What there are is 
Google Plus Communities but Google Groups are separate from Google Plus.
Google Groups: groups.google.com
Google Plus: plus.google.com
They are 2 separate things.
Also with Google Groups, you cannot get "followers". So your question is wrong.
With Google Groups you get users (members).
The same applies to Google Plus Communities too.
The only thing in Google you can get "followers" on is your Google Plus Profile or Google Plus Page.
Even then they're not called 
followers they're called 
Circles. (Even though they are basically followers or friends).
So again, your question hasn't been asked right.
Please think about the question you're asking and then ask it again in the right way for the right thing.
Let's presume you asked "How to increase my Google Group members?".
For that I would say, the same way as you increase circles or members of your Page or Google Plus Community.
You will want to share that Group on other similar/related groups to yours.
Also add people on Google Plus in your niche and share with them your Google Group link.
You can also do marketing of it such as through social bookmarking, article marketing, document sharing, social networking.
Hope that helps.