Summary: An efficient and accurate numerical method for solving the well-known Black-Scholes equation in option pricing is presented in this article. The method can be used for cases in which the coefficients in the Black-Scholes equation are time-dependent and no analytic solutions are available. It is an extension to the method by the authors [“A new method for solving convection-diffusion equations”, Proceedings of the 11th IEEE International Conference on Computational Science and Engineering, IEEE Computer Society, Los Alamitos, CA, USA, 107–114 (2008)] for solving 1D convection-diffusion equations with constant diffusion and convection coefficients using the fourth-order Padé approximation on a 3-point stencil. The new method can handle equations with variable diffusion and convection coefficients that depend on \(x^2\) and \(x \), respectively, where \(x\) is the independent variable. Numerical examples are presented in the article to demonstrate the accuracy and efficiency of the method.