This article presents an efficient method for finding the numerical solution to time delay fractional optimal control problems using the fractional Chelyshkov wavelet. Here we have used fractional derivative ${^{C}}D_{{t}}^{\mu}$ in Caputo sense. With the help of Riemann Liouville fractional operational matrices and collocation points, the time delay optimal control problem is reduced into a system of algebraic equations. The Lagrange multiplier technique solves these equations and obtains the optimized value. The convergence analysis and error bounds of the proposed approach are also established. At last, to demonstrate the high precision of the numerical method, we examine several examples.