In hypersonic thermochemical nonequilibrium flow calculations, a large difference between the numerical time step and the molecular vibration relaxation time or the chemical reaction time can bring about serious numerical stiffness problems, which are exacerbated by grid refinement in strong interaction areas such as near-wall or corner. The initial maximum CFL number and convergence rate are thus limited under high Reynolds conditions. The original LU-SGS algorithm only considers the implicit treatment of the source term and convection term. Two fully implicit LU-SGS algorithms, the FLU-SGS algorithm and the BLU-SGS algorithm, were developed by deriving and implementing the diagonal approximation of the spectral radius of the viscous Jacobian matrix. The convergence speeds of the three algorithms were investigated in cases of high enthalpy two-dimensional cylinder flow and axisymmetric re-entry capsule flow. The results show that strong viscous interaction and large separation can be quickly established and 3~5 orders of increase of the maximum CFL number can be reached with FLU-SGS and BLU-SGS algorithms. Thus the newly developed algorithms are efficient in accelerating convergence in the calculation of complex thermochemical non-equilibrium flows.