This article presents a novel approach for solving the one-dimensional second-order telegraph equation along with Dirichlet boundary conditions. The method is based on the subdivision collocation technique, which discretizes the time derivative using a typical finite difference approach. The method employs the fundamental functions of the subdivision scheme as interpolating functions in space. To assess the scheme’s stability, the von Neumann (Fourier) method is utilized. The authors provide various test scenarios to demonstrate the accuracy of the new approach and the effectiveness of the subdivision collocation technique. The numerical results align well with previously established exact solutions and research. The proposed method offers numerous advantages, including computational efficiency, applicability, and precision. The article comprehensively discusses the procedure and presents results demonstrating its efficacy. This paper makes a significant contribution to the field of numerical approaches for telegraph equations.