- Sign in to Google Groups.
- Click the name of a group.
- On the left, click Members.
- At the top, click Add members.
- Enter the email addresses of the people to invite.
- (Optional) To add a welcome message to the email notification for new members, enter a message.
- Click Add members.
The members are added to the group, even if their names don't appear on the group member list immediately.
NOTE: If you try to add a user to a group and get an error message saying that their email address is the primary, secondary, or alternate address of an existing member, that user is already a group member.
Summarized from Google instructions on how to Add people to your Group Directly.