Large-scale traffic and transportation logistics analysis requires a realistic depiction of network traffic condition in a dynamic manner. In the past decades, vehicular traffic simulation approaches have been increasingly developed and applied to describe time-varying traffic dynamics. Most of the existing approaches are so-called microscopic simulation in which complex driving behaviors such as car following and lane-changing are explicitly modeling in second or sub-second time resolution. These approaches are generally challenging to calibrate and validate and they demand a vast amount of computing resources. This paper discusses a new Anisotropic Mesoscopic Simulation (AMS) approach that carefully omits micro-scale details but nicely preserves critical traffic dynamics characteristics. The AMS model allows computational speed-ups in the order of magnitudes compared to the microscopic models, making it well-suited for large-scale applications. The underlying simulation rules and macroscopic dynamical characteristics are presented and discussed in this paper.