The evolving economic and technological landscape has brought about significant changes in travel behaviors and traffic patterns. These changes have led to the emergence of complex, multi-modal travel demands that interact with transportation networks, posing new challenges in transportation analysis and control. The primary objective of this study is to address these challenges by improving transportation modeling and data completeness using advanced modeling tools and transportation big data. We propose a dual-driven simulation model that integrates transportation simulation and big data. The approach begins by utilizing initial Location-Based Services (LBS) data to establish a mesoscopic multi-modal simulation model, which is then calibrated. This calibrated model is then employed to complete the missing trajectories of the LBS data. The innovative aspect of this dual-driven simulation model lies in its novel approach to constructing transportation models and completing LBS data, thereby enhancing both the simulation accuracy and the results of missing path completion. We conduct tests using the urban area of Hangzhou as an example, and the results show that the Normalized Root Mean Square Error (NRMSE) between the average link speeds in the simulation model and in real world observation is reduced to 24.1%. In the LBS data completion process, our proposed method achieves a travel mode identification accuracy of 95.3% for private car travel. Compared to the two baseline methods, the average accuracy of completed trajectories increases by 6.31% and 2.46%, respectively.