This paper is concerned with iterative solutions to the generalized Sylvester matrix equation A₁ V + A₂ V + B₁ W + B₂ W = E₁ VF₁ + E₂ VF₂ + C. Two iterative algorithms are presented to obtain the reflexive and Hermitian reflexive solutions. With these iterative algorithms, for any initial reflexive and Hermitian reflexive matrices the solutions can be obtained. Some needed lemmas are first stated, then two theorems are stated and proved where the iterative solutions are obtained. Finally, we report two numerical examples to verify the theoretical results.