By replacing the typical no-slip boundary conditions with velocity slip and temperature jump boundary conditions, the predicting accuracy of the CFD modeling is improved effectively for high altitudes flow in the slip regime. The numerical iterations usually suffer form divergence when the Maxwell slip boundary conditions are implemented with very great number of grid points by the numerical method, which the velocity slip and temperature jump are evaluated through explicit calculation of the velocity and temperature gradient terms. In the theoretical analysis, it is shown that the explicit calculation of gradient terms displays the time advancement process of the Maxwell slip boundary conditions similar to a Jacobian iteration scheme, hence it must satisfy the condition of convergence. In order to remove the limitation from the condition of convergence, a numerical treatment which is convergent for arbitrary grid density was derived for the slip boundary conditions. Numerical tests were calculated to demonstrate the validity of the derived method. A space shuttle model was studied numerically for hypersonic flow at high altitudes. The results disagreement between the slip and no-slip conditions was compared and the influence of slip effects on vehicle aerodynamic characteristics and aerothermodynamic properties was analyzed. 