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• We proposed an iterative algorithm for a class of generalized coupled Sylvester-conjugate matrix equations over generalized Hamiltonian matrix. • We proved the proposed algorithm is finitely terminated. • Some numerical examples are tested to verify the efficiency and stability of the proposed algorithm. In this work, we present an iterative algorithm to solve a class of generalized coupled Sylvester-conjugate matrix equations over the generalized Hamiltonian matrices. We show that if the equations are consistent, a generalized Hamiltonian solution can be obtained within finite iteration steps in the absence of round-off errors for any initial generalized Hamiltonian matrix by the proposed iterative algorithm. Furthermore, we can obtain the minimum-norm generalized Hamiltonian solution by choosing the special initial matrices. Finally, numerical examples show that the iterative algorithm is effective. [ABSTRACT FROM AUTHOR]