This paper proposed a new tooth surface modeling method for beveloid gear based on the real cutter surface using two orthogonal variables. Then, the analytical mesh model with and without misalignments were derived and solved to study the influences of geometry design parameters on contact behaviors for paralleled beveloid gear pair. Loaded tooth contact analysis is used to validate the proposed mesh model by abaqus software, and the error is below 5%. Results suggest that the increase in pressure, cone, and helical angles enlarge the contact area for meshing without misalignments. The addendum coefficient has unsubstantial impacts on the contact behaviors. For meshing with axis error in the horizontal direction, the growth of pressure angle, cone angle, helical angle, and addendum coefficient improves the carrying capacity of single tooth. But the transmission error deteriorates with the increase in pressure, cone, and helical angles. All three types of misalignments have little influence on the size of the contact ellipse. The growth of axis errors in horizontal and vertical directions significantly increases the transmission error, but the center distance error has a little influence on the transmission precision.