Abstract: Based on the Gas-Kinetic Unified Algorithm (GKUA) for flows from rarefied transition to continuum, the effect of rotational non-equilibrium is investigated on the gas flow involving relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is treated as a new Boltzmann collision invariant, then the unified Boltzmann model equation involving rotational non-equilibrium effect is presented for various flow regimes. The molecular velocity distribution function is integrated by the weight factor on the energy of rotational motion, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions, then the numerical algorithm of the Boltzmann kinetic model equation involving rotational non-equilibrium effect is developed. As the applications of the GKUA, the supersonic and hypersonic flows of diatomic gas involving rotational non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.2≤Ms≤25, the two-dimensional erect plate and planar ramp flows with the whole of Knudsen numbers of 9×10-4≤Kn∞≤10 and the three-dimensional re-entering rarefied flow around a tine double-cone body. The computed results match the relevant experimental data, the results of the Generalized Boltzmann Equation (GBE) and Ellipsoidal Statistical (ES) model equation well. It has been validated that the unified algorithm in solving the Boltzmann model equation involving rotational non-equilibrium effect can simulate the one-, two- and three-dimensional gas flows covering various flow regimes well and truly. The non-equilibrium flow phenomena and mechanisms from high rarefied free-molecule to continuum covering the medium transition regimes are revealed and analyzed.