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This study focuses on the valuation of geometric Asian power options and presents an efficient numerical algorithm for solving the option price PDE. The analytical methodology utilizes the fractional Ito formula and replicating portfolio techniques to derive a PDE that characterizes the option price. However, due to the lack of an analytical solution for this PDE, a numerical method is proposed to solve it. The numerical solution involves implementing a time-semi-discrete scheme obtained through forward time difference approximation, while the other derivatives in the equation are approximated using cubic B-spline quasi-interpolation approximation. By employing the respective scheme and incorporating the initial and boundary conditions, the numerical solution for the equation is obtained. Subsequently, the stability of the method is investigated, and numerical results are presented. The main advantages of the presented method are its simplicity for computer implementation and its suitability for multi-dimensional problems.