Our paper presents a numerically robust control design algorithm for a class of Optimal Control Problem (OCPs). The computational approach we develop constitutes an extension of the celebrated Gauss pseudo-spectral method. The last one makes it possible to reduce the Pontryagin Maximum Principle related Hamiltonian boundary value problem to an auxiliary algebraic system. The implementable scheme we propose is numerically consistent (by implementation) and implies an effective robust control procedure for a relative small discretization grids. The pseudo-spectral methodology is used in combination with a classic differential continuation approach. The presented solution procedure can be extremely useful when a generic shooting-type solution method fails (the case of a high sensitivity or stiffness). We finally consider an illustrative example and discuss the obtained results.