A connector structure for a Schrader (American) valve or a Presta (French) valve contains an air connector connected with a Schrader (American) valve or a Presta (French) valve. The Schrader (American) valve includes Schrader (American) threads and a Schrader (American) inlet part; the Presta (French) valve includes Presta (French) threads and a Presta (French) inlet part. The air connector contains a body including a Schrader (American) inserting hole with a Schrader (American) screwing section, a Presta (French) inserting hole, a movable groove, an air intake, and at least one through orifice; a limiting block including a retaining segment with plural locking teeth and including a defining segment; a control set disposed on the body and controlling the defining segment; a stopping rod mounted in and limited by the movable groove, the stopping rod including a confining slot and an abutting segment which correspond to the Schrader (American) inserting hole.