This paper proposes Dual-LS, a novel continuous learning paradigm, to address the critical forgetting problem that arises in artificial intelligence (AI), particularly in vehicle movement prediction based on deep neural networks (DNNs), which form the foundation of smart city services. Existing solutions suffer from high data collection costs, low sample efficiency, and an inability to balance long-term and short-term experiences. Inspired by the complementary learning system of the human brain, Dual-LS combines two synergistic memory rehearsal and replay mechanisms to accelerate experience retrieval and dynamically adjust long-term and short-term knowledge representations. Experimental results using real-world data from three countries, over 770,000 vehicles, and a total of 11,187 km of cumulative test driving distance demonstrate that Dual-LS mitigates critical forgetting by up to 74.31%, reduces computational resource requirements by up to 94.02%, and significantly improves prediction stability without increasing data requirements. In conclusion, Dual-LS provides a computationally efficient and human-like continuous learning adaptability to DNN-based vehicle movement prediction, providing a suitable model for smart cities.