A computer simulation model is proposed for discretetime doubly-selective compound-K fading channel. It first generates multiple independent mobile-to-mobile Rayleigh fading Channel Impulse Response (CIR) using the nonisotropic scattering model, then generates the cross- and auto-correlated gamma shadowing matrix using the combination of the memoryless nonlinear transformation (MNLT) method and the decomposition methods. It then combines the complex Rayleigh CIR with the gamma shadowing matrix to yield the doubly-selective fading channel CIR whose envelop follows the compound K distribution. Simulation examples demonstrate that the proposed method can effectively produce compound K fading channel responses with satisfactory statistical properties.