A methodology is described for solving optimal pointwise control of a coupled system of Burgers' equations. It is aimed to determine the optimal pointwise control that minimizes a given performance measure. The performance measure is specified as a quadratic functional of the distance between a final state function and a predefined target function along with the energy due to the control effort. The modal expansion method is used to reduce the optimal control of distributed parameter systems into the control of the invariant lumped parameter systems. A system of non-linear algebraic equations are derived as necessary conditions of optimality and solved by Runge-Kutta method to obtain the optimal Fourier coefficients and frequencies. The feasibility of the proposed methodology is demonstrated by numerical simulations.