We establish a new finite volume scheme for a second order hyperbolic equation with several time independent delays in any space dimension. This model is considered in [7] where some exponential stability estimates are proved and in [8] which dealt with the oscillation of the solutions. The delays are included in both the exact solution and its time derivative. The scheme uses, as space discretization, SUSHI (Scheme using Stabilization and Hybrid Interfaces) developed in [5]. We first prove the existence and uniqueness of the discrete solution. We subsequently, develop a new discrete a priori estimate. Thanks to this a priori estimate, we prove error estimates in several discrete seminorms. This work is an extension and improvement of our recent work [2] which dealt with the finite volume approximation of the wave equation but with only one delay which is included in the time derivative of the exact solution.