Abstract: An approach is presented through minimizing the distance function between P_n,m(u,v) and Q_n1,m1(u,v）(n₁≤ n-1,m₁≤ m-1） over unit square ［0,1］×［0,1］ in the sense of least squares normal (L₂）,which gives the explicit representation of control points\left\q_i j\right\_i=0, j^n 1, m_1=0 of the reduced multi-degree tensor product Bézier surface Q_n1,m1(u,v）.During the multi-degree reduction process,we also consider two cases,one has the constraint of high-order interpolations over corners and another without any constraint.Examples show that the proposed approach has better approximation of the reduced surfaces than that of current methods.