In order to investigate the effects of linear shear flow on characteristics of flow past a square cylinder, a numerical model for shear flow past a square cylinder was established by introducing the convective outflow boundary condition into the characteristic-based operator-splitting finite element method. The reliability of the numerical model was verified through simulation of the uniform flow past a square cylinder. The numerical results show that the shear parameter k has a significant effect on the two rows of vortices in the wake of flow past the square cylinder, and a larger k value inhibits the vortex shedding from the cylinder. When k≥0. 4, the formation region of vortices behind the cylinder becomes a triangular zone. As the value of k increases, the stagnation point shifts towards the lateral separation point. When k≥0. 3, the location of the stagnation point remains unchanged. The significant change in the mean drag coefficient occurs in the range 0. 2 ≤k≤0. 25. When k≥0. 2, the mean lift coefficient is negative.