A new tooth profile curve equation of the cycloid gear is proposed based on the gear meshing transmission principle. Due to the problem that complex cycloid equation is difficult to be substituted directly with the software for modeling, the method of designing the cycloid gear tooth profile curve is obtained by using data fitting. Therefore, the solution to repair the cycloid gear is suggested. The method is simple in principle and has significant and practical value for the design and manufacturing of the cycloid speed reducer.