<p>In this study, the spectral difference method is implemented for the numerical solution of the discrete Boltzmann equation to provide a robust and high-order accurate compressible gas kinetic scheme for effectively computing compressible rarefied gas flows. To this aim, the discrete Boltzmann equation with the Shakhov model is considered and the spatial discretization in the resulting equation is performed by the spectral difference method and the fourth-order Runge-Kutta method is used for the temporal discretization. Different one- and two-dimensional test cases are simulated to examine the accuracy and performance of the present methodology based on the spectral difference solution of the Boltzmann equation (SDBE). At first, the two-dimensional incompressible flow problems, namely, the Taylor-Green vortex flow and the cavity flow are simulated by applying the third-order SDBE and the results obtained are compared with the analytical solution and the available gas-kinetic and direct simulation Monte Carlo (DSMC) results which exhibit good agreement. Then, some compressible flow problems including the one-dimensional Riemann shock tube, the one-dimensional normal shock structure and the supersonic flow over a cylinder problem are computed to better examine the accuracy and robustness of the present method by applying the SDBE in different conditions. To further assess the accuracy and performance of the third-order SDBE, the simulations are also performed by the third-order upwind finite-difference solution of the Boltzmann equation (UFDBE) and the results of these two numerical schemes are thoroughly compared with each other. It is indicated that the high-order gas kinetic scheme implemented based on the spectral difference solution of the Boltzmann equation (SDBE) can be applied for accurately and effectively computing rarefied gas flows in a wide range of Knudsen numbers.</p>