Currently, the global situation of COVID-19 is aggravating, pressingly calling for efficient control and prevention measures. Understanding spreading pattern of COVID-19 has been widely recognized as a vital step for implementing non-pharmaceutical measures. Previous studies investigated such an issue in large-scale (e.g., inter-country or inter-state) scenarios while urban spreading pattern still remains an open issue. Here, we fill this gap by leveraging the trajectory data of 197,808 smartphone users (including 17,808 anonymous confirmed cases) in 9 cities in China. We find a universal spreading pattern in all cities: the spatial distribution of confirmed cases follows a power-law-like model and the spreading centroid is time-invariant. Moreover, we reveal that human mobility in a city drives the spatialtemporal spreading process: long average travelling distance results in a high growth rate of spreading radius and wide spatial diffusion of confirmed cases. With such insight, we adopt Kendall model to simulate urban spreading of COVID-19 that can well fit the real spreading process. Our results unveil the underlying mechanism behind the spatial-temporal urban evolution of COVID-19, and can be used to evaluate the performance of mobility restriction policies implemented by many governments and to estimate the evolving spreading situation of COVID-19.