To optimize the shape of square cylinder, Large-eddy Simulation is applied in the study of flow past square cylinders at a high Reynolds Number Re of 22 000. The cylinders have various combinations of sharp/round corners and flat/concave/bulging edges. Particularly，the aerodynamic characteristics of cylinders with a combination of round corners and bulge edges are studied with the changing curvature radius of the edge. Besides, the flow patterns are discussed in detail to reveal the mechanism of aerodynamic optimization. The results show that corner and side modifications can significantly alter the structure of flow around cylinders and influence the aerodynamic performance of cylinders. In comparison to the concave modification, the round modification and bulge modification can reduce the aerodynamic forces, overall surface pressures and vortex shedding intensity of cylinders considerably. Among cylinders with various combinations of shape modifications, the cylinder with rounded corner and bulge edge leads to a thinner shear layer and a smaller recirculation region at the upper and lower sides of cylinder. Besides，it also causes a longer wake length, a weaker vortex shedding and reduces the aerodynamic forces. A further research shows that the aerodynamics of the round-bulge cylinder is extremely sensitive to the curvature radius of the edge. There exists an optimal curvature radius, which results in the lowest aerodynamic forces，the highest Strouhal number, the longest length of the recirculation region, and the weakest vortex shedding intensity.