Convergence rates of the original LU-SGS scheme and its modified methods were investigated and compared under hypersonic conditions, which is aimed to implement the LU-SGS algorithm efficiently for numerical simulation of complex geometries in engineering environment. Numerical results of 2D cylinder, 3D blunt cone and space shuttle show that: the viscous terms must take the implicit form for hypersonic viscous flows. the convergence rate of the BLU-SGS inner iterations is fast than that in the DP-LUR method. Jacobian matrices in the LU-SGS algorithm have a significant effect on computational work and convergence performance. for the flows without separation, fast convergence can be reached by using the exact matrix method and for the flows with large separation, numerical instability makes the exact matrix method less efficient than the diagonal method.