As a key technique in distributed systems, time synchronization plays an important role in time sensitive modern industrial wireless local area networks (WLANs). Based on time packet exchange technology, the IEEE 1588 precise time protocol (PTP) achieves high precise and low power consumption time synchronization in wired Ethernet. In WLANs, however, it is difficult for the wireless sensor nodes to acquire accurate timestamps due to their limited resources. Moreover, compared to wired Ethernet, WLANs suffer more from wireless channel sharing, fading and packet collisions, which leads to overwhelming transmission delay jitters. Therefore, analytic solution to PTP's performance in WLANs is very difficult and it is of importance to evaluate PTP's performance by realistic simulation. In this paper, based on the open source OMNeT++ simulation engine, we present the simulator we developed for PTP time synchronization in 802.11 WLANs. The behavior of the PTP time synchronization, the simulation results and the factors that affect the PTP performance are presented and evaluated.