Understanding the urban mobility patterns is essential for the planning and management of public infrastructure and transportation services. In this paper we focus on taxicab moving trajectory records and present a new approach to modeling and analyzing urban mobility dynamics. The proposed method comprises two phases. First, discrete space partition based on flexible grid is developed to divide urban environment into finite nonoverlapping subregions. By integrating mobility origin-destination points with covered region, the partitioned discrete subregions have better spatial semantics scalability. Then, we study mobility activity and its distribution randomness during given time periods among discrete subregions. Moreover, we also carry out the analysis of mobility linkage of mobility trips between different regions by O-D matrix. We present a case study with real dataset of taxicab mobility logs in Shenzhen, China, to demonstrate and evaluate the methodology. The experimental results show that the proposed method outperforms the clustering partition and regular partition methods.