In this paper, an accelerated Jacobi-gradient based iterative (AJGI) algorithm for solving Sylvester matrix equations is presented, which is based on the algorithms proposed by Ding and Chen [6], Niu et al. [18] and Xie et al. [25]. Theoretical analysis shows that the new algorithm will converge to the true solution for any initial value under certain assumptions. Finally, three numerical examples are given to verify the efficiency of the accelerated algorithm proposed in this paper.