We focus on the numerical investigation of a water wave model with a nonlocal viscous dispersive term. We construct and analyze a schema to numerically solving the nonlocal water wave model. The key for the success consists in a particular combination of the treatments for the nonlocal dispersive term and nonlinear convection term. The proposed methods employ a known $(2-\alpha)$-order schema for the $\alpha$-order fractional derivative and a mixed linearization of the nonlinear term. A rigorous analysis shows that the proposed schema is unconditionally stable, and the linearized  Crank-Nicolson plus $(2-\alpha)$--order schemes is ${O}( \Delta t^{\frac{3}{2}} +N^{1-m})$. A series of numerical examples is presented to confirm the theoretical prediction. Finally the proposed methods are used to investigate the asymptotical decay rate of the solutions of the nonlocal viscous wave equation, as well as the impact of different terms on this decay rate.