A golf club head with a club head body having an external surface with a heel portion, a toe portion, a crown portion, a sole portion, and a front opening is described. A face insert support structure is located at the front opening. The support structure includes a peripheral member and a rear support member. The rear support member has a front surface and a rear surface. A face insert is attached at the front opening and closes the front opening of the body. An undercut fill structure is attached to a portion of the rear surface of the rear support member.