For the location selection problem of urban logistics distribution centers, considering urban dynamic development scenarios and unmanned aerial vehicle (UAV) characteristics is crucial for improving the scientificity and practicality of location schemes. First, three dynamic demand scenarios, namely natural growth, ring expansion, and directional development, were established according to urban development patterns. A full-coverage location model with the objective of minimizing the sum of location cost and operating cost was then constructed. Next, to improve the solution accuracy of the model, the traditional K-means clustering algorithm was improved by using a grid-based method. Finally, numerical simulations verified the feasibility and effectiveness of the model and algorithm. The results show that the improved K-means clustering algorithm achieves better clustering performance; the total cost of distribution centers under the dynamic strategy is lower than that under the static strategy; and except for extremely special scenarios (e.g., abnormally high construction cost or newly added demand completely concentrated in a single year), the dynamic strategy is the better choice.