Abstract: A three level compact finite difference scheme for solving a one-dimensional viscous wave equation is derived. Using the energy method for error analysis, it is proved that the difference solution converges to exact solution with a convergence order of O(τ²+h⁴) in the maximum norm. Moreover, the Richardson extrapolation method is utilized to make the final solution fourth-order accurate in both time and space. Finally, a numerical example is provided to verify the convergence order and validity of the difference scheme.