Summary: The Sylvester matrix equation \(AX+YB=C\) with two unknown matrices \(X, Y\) is discussed. By applying a hierarchical identification principle, we propose an iterative algorithm for solving the least norm problem of the equation. We prove that the iterative solution converges to the least-squares solution and the least-squares solution with the minimum norm for some initial values. Furthermore, the iterative method is extended to solve the least Frobenius norm problem of a general matrix equation. Finally, the algorithm is tested on a computer and the results verify the theoretical findings.