The constrained matrix equation problem has a wide range of applications in control theory, vibration theory, engineering and science computing. In this paper, an algorithm is constructed to solve a kind of matrix equations over centro-symmetric matrices with a constrained submatrix. The least squares centro-symmetric solutions of the matrix equations with a constrained submatrix can be obtained within a finite number of iterations in the absence of round-off errors, and the least-norm least squares centro-symmetric solution with the constrained submatrix can also be obtained by choosing a special kind of initial matrices. Numerical examples show that the convergence speed of the proposed algorithm is fast.