The stationary Wigner equation (SWE) is often used to model the quantum transport in semiconductor devices. The discrete stationary Wigner equation is derived using the first-order upwind scheme and the sinc-Galerkin method [H. Jiang, T. Lu, and W. Zhang, J. Comput. Appl. Math. 409 (2022), 114152]. Based on the successive over relaxation (SOR) iterative method, we develop the basic SOR-like (BSOR-like) and updated SOR-like (USOR-like) iterative methods for solving the discrete stationary Wigner equation efficiently. The main difference between these two iterative methods is that the USOR-like iterative method aims to make more use of the updated components of the Wigner function by splitting the pseudo-differential term. The convergence range of the relaxation parameter in the USOR-like iterative method is numerically investigated. Compared with that of the BSOR-like iterative method, this interval is significantly enlarged. Numerical results have also shown that the USOR-like iterative method is more computationally efficient than the BSOR-like iterative method. As an application, the resonant tunneling effect and the effects of scattering are investigated by simulating a resonant tunneling diode (RTD) using the USOR-like iterative method.