Current beveloid gears' tooth thickness variation is achieved by changing modification coefficient, so the intersecting lines between the tooth profile and any arbitrary cross section perpendicular to the gear's axis are differ-ent segments of the same involute, which leads to the gear producing a certain conical degree along the gear's axial direction. A new base circle moved heveloid gear (BCMBG) is presented in this paper, which is realized through moving the base circle. BCMBG has the same tooth depth in the tooth direction and the intersecting lines between the tooth profile and any arbitrary cross section perpendicular to the gear's axis are the same segment of an involute, eliminating the possible interference in the clearance adjusting process of conventional beveloid gears. Firstly, tooth surface equations of the new beveloid gear are derived, in which parameter θ determines tooth thickness's variation quantity. In addition, the discrete data is obtained by using Matlab and then imported into Pro/E to establish the beveloid gear's accurate geometric model, according to which the prototype of the proposed beveloid gear is made to verify the tooth surface equations. Finally, the contact model of the heveloid gear's tooth surface at the transmission pair is constructed, and the transient contact points and contact lines are calculated with Matlab.