This paper describes a computationally efficient parallel-computing framework for mesoscopic transportation simulation on large-scale networks. By introducing an overall data structure for mesoscopic dynamic transportation simulation, we discuss a set of implementation issues for enabling flexible parallel computing on a multi-core shared memory architecture. First, we embed an event-based simulation logic to implement a simplified kinematic wave model and reduce simulation overhead. Second, we present a space-time-event computing framework to decompose simulation steps to reduce communication overhead in parallel execution and an OpenMP-based space-time-processor implementation method that is used to automate task partition tasks. According to the spatial and temporal attributes, various types of simulation events are mapped to independent logical processes that can concurrently execute their procedures while maintaining good load balance. We propose a synchronous space-parallel simulation strategy to dynamically assign the logical processes to different threads. The proposed method is then applied to simulate large-scale, real-world networks to examine the computational efficiency under different numbers of CPU threads. Numerical experiments demonstrate that the implemented parallel computing algorithm can significantly improve the computational efficiency and it can reach up to a speedup of 10 on a workstation with 32 computing threads.