Reservoir computing (RC) is a highly efficient network for processing spatiotemporal signals due to its low training cost compared to standard recurrent neural networks. The design of different reservoir states plays a very important role in the hardware implementation of RC system. Recent studies have used the device-to-device variation to generate different reservoir states; however, this method is not well controllable and reproducible. To solve this problem, we report a dynamic memristor-based RC system. By applying a controllable mask process, we reveal that even a single dynamic memristor can generate rich reservoir states and realize the complete reservoir function. We further build a parallel RC system that can efficiently handle spatiotemporal tasks including spoken-digit and handwritten-digit recognitions, in which high classification accuracies of 99.6% and 97.6% have been achieved, respectively. The performance of dynamic memristor-based RC system is almost equivalent to the software-based one. Besides, our RC system does not require additional read operations, which can make full use of the device nonlinearity and further improve the system efficiency. Our work could pave the road towards high-efficiency memristor-based RC systems to handle more complex spatiotemporal tasks in the future.