In this paper, a class of improved methods based on non-polynomial cubic splines in space and finite difference in time direction are constructed for the second-order hyperbolic equations with initial boundary value problems. Truncation error and stability analysis of the methods have been carried out. It is shown that by suitably choosing the parameters, many known methods can be derived from ours. We also obtain a new high accuracy scheme of , which is conditionally stable for .Finally, a numerical experiment is tested and results are compared with other published numerical solutions.