Artificial intelligence underpins most smart city services, yet deep neural network (DNN) that forecasts vehicle motion still struggle with catastrophic forgetting, the loss of earlier knowledge when models are updated. Conventional fixes enlarge the training set or replay past data, but these strategies incur high data collection costs, sample inefficiently and fail to balance long- and short-term experience, leaving them short of human-like continual learning. Here we introduce Dual-LS, a task-free, online continual learning paradigm for DNN-based motion forecasting that is inspired by the complementary learning system of the human brain. Dual-LS pairs two synergistic memory rehearsal replay mechanisms to accelerate experience retrieval while dynamically coordinating long-term and short-term knowledge representations. Tests on naturalistic data spanning three countries, over 772,000 vehicles and cumulative testing mileage of 11,187 km show that Dual-LS mitigates catastrophic forgetting by up to 74.31\% and reduces computational resource demand by up to 94.02\%, markedly boosting predictive stability in vehicle motion forecasting without inflating data requirements. Meanwhile, it endows DNN-based vehicle motion forecasting with computation efficient and human-like continual learning adaptability fit for smart cities.