Cross-city point of interest (POI) recommendation for tourists in an unfamiliar city has high application value but is challenging due to the data sparsity. Most existing models attempt to alleviate the sparsity problem by learning the user preference transfer and drift. However, they either fail to simultaneously model the preference transfer and drift in both long- and short-term user preferences or cannot accomplish the task of the next POI recommendation, which is crucial for a wide spectrum of applications ranging from transportation and urban planning to advertising. To address the limitation, we proposed a user preference transfer and drift network (UPTDNet) for cross-city next POI recommendation. UPTDNet excels at cross-city recommendations by learning the transfer and drift of both long- and short-term preferences. For short-term preference, dual recurrent neural network-based (RNN-based) branches are designed to model preference transfer from tourist’s current city and drift among different user roles. For long-term preference, a mapping function and user similarity calculation are employed for preference transfer from the tourist’s home city and drift among individual users. Experiments are conducted on the Gowalla and Foursquare datasets, and the results show that UPTDNet consistently and significantly outperforms state-of-the-art models by an average of 10.22% to 22.63% in the next POI recommendation task. Ablation study and further analysis validate the effectiveness and plausibility of considering both user preference transfer and drift in the cross-city recommendation.