Hangouts by their nature are generally open to anyone to join in the Circles you start them in but what if you want to have a private Hangout session with only selected people? There is no feature in Google+ that allows you to do this but there is a way to achieve this.
You can do this by creating a new Circle which you will use for this purpose only and you can add just those people you wish you Hangout with. What you must remember here is one of the fundamental things about Circles – just because you add someone to a Circle it doesn’t mean they will see posts from you. They need to have you in their Circle(s) also to be able to see the Hangout when you start it so you’ll need to ensure you’ve got this worked out beforehand.
So the steps to achieve this are:
1. Create a new Circle for your private Hangout (if you don’t already have one) and you can call it something like Private Hangout.
2. Add just those people you want to Hangout with in your private session to this circle
3. Go to your Stream and click the Start a Hangout link
4. You will now be taken to the Hangout Green Room to get ready to start the Hangout. Ensure that you select only the Private Hangout Circle in the box where it says Who do you want to Hangout with? This is the important step to restrict it just to the people you want.
5. Click the Hang out button to start the session and wait for the others to join
Once you’re done you can either leave the people in that Cirlce if you’re going to be Hanging out with them again or you can remove them and leave the Circle empty to allow you to add different people for a future private hangout.
So there you have it, while there is no feature in Google+ to allow you have private hangouts by creating a Circle with just those people who you want to Hangout with and then starting the Hangout for just that Circle does the trick.