Abstract The present paper uses new approach and methodology to solve second order one dimensional hyperbolic telegraph equation numerically by B-spline collocation method. It is based on collocation of modified cubic B-spline basis functions over the finite elements. The given equation is decomposed into system of equations and modified cubic B-spline basis functions have been used for spatial variable and its derivatives, which gives results in amenable system of differential equations. The resulting system of equation subsequently has been solved by SSP-RK54 scheme. The efficacy of proposed approach has been confirmed with numerical experiments, which shows the results obtained are acceptable and in good agreement with earlier studies. The advantage of this scheme is that it can be conveniently used to solve the complex problems and it is also capable of reducing the size of computational work.