<p>In this paper, a new numerical scheme based on the weighted and shifted Grünwald-Letnikov operators with Bernoulli polynomials, is proposed for time distributed-order and space Riesz variable-order fractional damped diffusion-wave equation. In the temporal direction, the distribution-order integral is first discretized into a sum of multi-term Captuo fractional derivatives by the quadrature formula, and then these fractional derivatives are approximated by using the weighted and shifted Grünwald-Letnikov operators. In the next, to obtain a full-discrete scheme, we use the Bernoulli polynomials combined with Gauss-Jacobi quadrature formula to approximate the Riesz variable-order fractional derivatives in the spatial direction. Furthermore, the stability and second-order convergence of the discrete scheme are discussed, and the error bounds of the numerical solutions are further analyzed. Finally, some numerical results are provided to show the accuracy and efficiency of the proposed method.</p>