Optimal control theory is an important branch of modern control theory which has been widely applied in various sciences. Uncertain optimal control is a theory dealing with optimal control problems which are based a new uncertainty theory and differs from the stochastic optimal control based on probability theory and fuzzy optimal control based on fuzzy set theory or credibility theory. As the further work of the uncertain optimal control with jump in the one-dimensional case and multidimensional linear-quadratic (LQ) uncertain optimal control problem with jump which has a quadratic objective function for a linear uncertain control system with jump, a general uncertain optimal control problem with n jumps in the multi-dimensional cases is considered in this paper. The principle of optimality is presented and the equation of optimality is obtained about multidimensional uncertain optimal control with n jumps. Finally, as an application, an optimal control problem in R&D (Research and Development) fiscal subsidy policy is discussed and the optimal control decisions are obtained.