Current studies on noncircular gears have focused primarily on geometric design, but equations for tooth surfaces are lacking. This limitation prevents tooth contact analysis (TCA) from being performed. This study investigates the mathematical model, including tooth surface equations for the design and TCA for tooth surface traits, of helical noncircular gears based on gear meshing theory. First, the gear shaping method was generalized to a helical noncircular gear design, and parametric tooth surface equations were proposed with generality. Compared with generating geometric models of noncircular gears, the proposed mathematical design method offers greater efficiency and accuracy. Second, the tooth section shapes were calculated according to the tooth surface equations. The gear exhibited varying tooth shapes at different end sections even if they were in the same gear teeth. Mathematical proofs demonstrated that the tooth surface of this gear is a developable surface with a straight line as the baseline. Furthermore, the tooth surface was curved in one principal direction only. Finally, the correctness of the helical noncircular gear tooth surface equations was verified via transmission experiments.