To study aerodynamics of spacecraft reentry covering various flow regimes, a Gas-Kinetic Unified Algorithm (GKUA) has been presented by computable modeling of the collision integral of the Boltzmann equation over tens of years. On this basis, the rotational and vibrational energy modes are considered as the independent variables of the gas molecular velocity distribution function, a kind of Boltzmann model equation involving in internal energy excitation is constructed by decomposing the collision term of the Boltzmann equation into elastic and inelastic collision terms under the conservation of the summation invariant and the H-theorem, in which the inelastic collision term is divided into translational-rotational and translational-rotational-vibrational energy relaxation according to a certain relaxation rate. Then, a set of controlling equations involving vibrational non-equilibrium effect can be got by introducing three reduced velocity distribution functions to cut back the number of independent variables. The gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions by developing the discrete velocity ordinate method and numerical quadrature technique. The gas-kinetic boundary conditions in thermodynamics non-equilibrium and numerical procedures are implemented by directly acting on the discretized velocity distribution functions, and then the unified algorithm of the Boltzmann model equation involving thermodynamics non-equilibrium effect is presented for the whole range of flow regimes.