Abstract: Based on the gas-kinetic unified algorithm (GKUA) from rarefied transition to continuum, numerical simulation technique for unsteady flows covering various flow regimes was developed by solving the Boltzmann-Rykov model equation involving molecular rotational degrees of freedom. The Rykov kinetic equation involving the effect of molecular rotational energy can be transformed into two kinetic governing equations with inelastic and elastic collisions by integrating the molecular velocity distribution function with the weight factor on the energy of rotational motion. The simultaneous equations were numerically solved by the discrete velocity ordinate (DVO) method in velocity space. Third-order WENO scheme was adopted for the physical space, and third-order explicit Runge-Kutta method was used for time evolution. Numerical simulation of the classical planar Karman vortex street was then implemented, to verify the adaptability of this unsteady simulation method on the low-speed flows in continuum.