A bevel gear pair with constant meshing characteristics with a constructed tooth pair is provided. The bevel gear pair with a constructed tooth pair includes a bevel gear I with a constructed tooth pair and a bevel gear II with a constructed tooth pair based on conjugate curves. In the present disclosure, a normal tooth profile curve of the bevel gear I with a constructed tooth pair and a normal tooth profile curve of the bevel gear II with a constructed tooth pair are continuous combined curves with the same curve shape, which facilitates machining by the same cutter. A common normal at an inflection point or a tangent point of the continuous combined curve passes through a pitch point of the bevel gear pair with a constructed tooth pair, and a position of the inflection point or the tangent point can be adjusted according to an actual demand.