In this paper we study an approximation scheme for a class of controlproblems involving an ordinary control v, an impulsivecontrol u and its derivative $\dot u$ . Adopting a space-timereparametrization of the problem which adds one variable to the statespace we overcome some difficulties connected to the presence of $\dot u$ .We construct an approximation scheme for that augmented system, prove that it converges to the value function of the augmentedproblem and establish an error estimates in L ∞ for thisapproximation. Moreover, a characterization of the limit of the discreteoptimal controls is given showing that it converges (in a suitable sense)to an optimal control for the continuous problem.