An nxn real matrix P is said to be a symmetric orthogonal matrix if P = P^–1 = P^T. An nxn real matrix X is called a generalized centro-symmetric matrix with respect to P, if X = PXP. It is obvious that every nxn matrix is also a generalized centro-symmetric matrix with respect to I (identity matrix). In the present paper, we propose a gradient-based iterative algorithm to solve the generalized coupled Sylvester matrix equations over the generalized centro-symmetric matrix pair (X₁,X₂). It is proved that the iterative method is always convergent for any initial generalized centro-symmetric matrix pair (X₁(1),X₂(1)). Finally, a numerical example is discussed to illustrate the results.