Laser cleaning is an advanced cleaning technology which is widely used in the manufacturing industry. Compared with the common planar laser cleaning process, the laser cleaning process of curved surface is difficult to control the completeness and homogeneity of the cleaning layer, which has a great influence on the surface quality and mechanical properties of the cleaned parts. Therefore, a three-dimensional numerical model of the laser cleaning process of the curved surface considering the coordinate system transformation of the heat source is established in this paper to clean the alumina on the surface of the 5754 aluminum alloy. The temperature distribution characteristics for different tangent slopes of the laser cleaning path and the temperature variation with time for different cleaning paths of the laser cleaning process are analyzed. The results show that the proposed method can provide important guiding significance for the practical laser cleaning process of the curved surface.