Numerical analysis is performed for a normal shock wave in a polyatomic molecule gas based on molecular gas dynamics, where the polyatomic gas is taken to be nitrogen. We adopt the polyatomic version of Gaussian-BGK Boltzmann equation for nitrogen gas and it is solved numerically with a finite difference method. The results agree well with the experimental results by Robben and Talbot (1966) at the shock Mach number 1.71. Furthermore, we examine the transition of rotational energy in the shock wave in terms of velocity distribution functions.