This paper presents a learning-based approach for impromptu trajectory tracking of non-minimum phase systems — systems with unstable inverse dynamics. In the control systems literature, inversion-based feedforward approaches are commonly used for improving the trajectory tracking performance; however, these approaches are not directly applicable to non-minimum phase systems due to the inherent instability. In order to resolve the instability issue, they assume that models of the systems are known and have dealt with the non-minimum phase systems by pre-actuation or inverse approximation techniques. In this work, we extend our deepneural-network-enhanced impromptu trajectory tracking approach to the challenging case of non-minimum phase systems. Through theoretical discussions, simulations, and experiments, we show the stability and effectiveness of our proposed learning approach. In fact, for a known system, our approach performs equally well or better as a typical model-based approach but does not require a prior model of the system. Interestingly, our approach also shows that including more information in training (as is commonly assumed to be useful) does not lead to better performance but may trigger instability issues and impede the effectiveness of the overall approach.