In this paper, a numerical approach is introduced for solving the one-dimensional sine-Gordon equation by employing the collocation method with septic B-splines. The stability of the proposed schemes is analyzed using the von Neumann method, showing conditional stability. To evaluate their accuracy, error norms are calculated, and numerical results are provided for two test cases. The results are compared with exact solutions and other numerical methods, demonstrating small absolute errors and confirming the convergence properties of the proposed approach.