The main aim of this study is to present a computational method based on Fibonacci polynomials for solving fractional nonlinear optimal control problems, where this scheme is applied to solving the optimal control problems of cancer treatment. Here, a pseudo-operational matrix of fractional integration is presented for the considered polynomials. Then, we use this matrix, the Gaussian quadrature rule, and the collocation method to reduce the given problem into a system of algebraic equations. The effectiveness of the present technique is tested by means of one example, and the results confirm its good performance.