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Static traffic assignment (STA) models have been widely utilized in the field of strategic transport planning. However, STA models cannot fully represent the dynamic road conditions and suffer from inaccurate assignment during traffic congestion. At the same time, an increasing number of installed sensors have become an important means of detecting dynamic road conditions. To address the shortcomings of STA models, we integrate multi-source traffic sensor datasets and propose a novel data-driven quasi-dynamic traffic assignment model, named DQ-DTA. In this model, records of toll stations are used for time-varying travel demand estimation. GPS trajectory datasets of vehicles are further used to calculate the dynamic link costs of the road network, replacing the imprecise Bureau of Public Roads (BPR) function. Moreover, license plate recognition (LPR) data are used to design a statistical probability-based multipath assignment method to capture travelers' route choices. The expressway network in the Hunan province is selected as the study area, and several classic STA models are also chosen for performance comparison. Experimental results demonstrate that the accuracy of the proposed DQ-DTA model is about 6% higher than that of the chosen STA models. [ABSTRACT FROM AUTHOR]