This paper discussed a modified gradient-based iterative (MGI) algorithm for solving the Sylvester conjugate transpose matrix problem over the Hamiltonian matrix. We proved that the suggested algorithm converges to the exact solution for every given initial Hamiltonian matrix. A sufficient condition is specified to assure that the suggested algorithm's solution converges to the Hamiltonian solution. Numerical examples are presented to verify the theoretical conclusions and illustrate the superiority and efficiency of the offered approach over the relaxed gradient-iterative (RGI) algorithm proposed in [13].