The invention relates to the technical field of cycloidal gear machining, and specifically relates to a method for modifying the tooth profile of a cycloidal gear through a catenary method, the cycloidal gear, and a speed reducer. The modifying method comprises the following steps: 1) determining a distribution rule between a pressure angle and an engagement phase angle at each point in the toothprofile of the cycloidal gear; 2) obtaining the modification amounts of the point with the smallest pressure angle, a tooth top and a tooth root; 3) establishing a first catenary equation of the relationship between the pressure angles and the modification amounts of the tooth profile points in a range from a modification reference point to the tooth top by taking the pressure angles and the modification amounts of the modification reference point and the tooth top as two end points; and establishing a second catenary equation of the relationship between the pressure angles and the modification amounts of the tooth profile points in a range from a modification reference point to the tooth root by taking the pressure angles and the modification amounts of the modification reference point and the tooth root as two end points; 4) obtaining the modification amounts of the points of the tooth profile of the cycloidal gear according to the first catenary equation, the second catenary equation and the distribution rule; and 5) subtracting the respective corresponding modification amounts in the normal direction of the tooth profile points of the cycloidal gear to obtain the modified toothprofile of the cycloidal gear.