The dynamic optimization or optimal control problem is more difficult to solve than the static optimization problem. This is because the conventional, classical method of solving the optimal control problem is as a two point boundary value problem, which needs split boundary conditions to be satisfied. This paper is a review of a recent, promising method known as the pseudospectral method for solving the optimal control problem. The states and control are parameterized as Chebyshev polynomials, and the solution found using the well developed static optimization theory. To demonstrate the effectiveness of the new method, an analytically solvable optimal control problem is solved by the Chebyshev polynomial method, which compares favourably with the analytical solution. © Research India Publications.