Abstract: Discrete ordinates method is one of main numerical methods for solving neutron transport equation, and spatial discretization and its error control are essential for computational accuracy. Traditional finite difference methods possess unphysical oscillations for specific circumstances and inaccuracy under coarse meshes limits their application. Step and linear short characteristic methods for the S_N equation were proposed. Short characteristic methods construct angular flux distribution based on characteristic solution according to spatial moment conservation of transport equation. Numerical verification and sensibility analysis about mesh size were conducted. Results of short characteristic method are in good agreement with the references. Results indicate that linear short characteristic scheme is less sensitive to mesh size and gains better accuracy over step short characteristic and other low-order difference methods.