The IEEE 802.11 wireless local area networks (WLANs) standard supports several equal-capacity communication channels which can be simultaneously shared and accessed by mobile stations. In such multichannel communication system, a mobile station basically can transmit on any of these channels based on a suitable access control protocol. However, with the feature of one transceiver per mobile station, the standard restricts mobile stations to operate in one selected channel and the other channel capacities are wasted inevitably. In this paper, we propose a new carrier sense multiple access (CSMA) based protocol, called multichannel access protocol (MAP), to support parallel transmissions in IEEE 802.11 ad hoc WLANs. To realize the proposed MAP protocol over contemporary ad hac WLANs, the MAP protocol is not only compliant with the IEEE 802.11 standard but also taking one transceiver constrain into consideration. All mobile stations with MAP will contend for channel access right in a dedicated channel during a periodical contention reservation interval (CRI) and then transmit data frames over different channels by a channel scheduling algorithm (CSA). Given a number of requests, the problem of finding a proper schedule for these requests to be served on a multichannel system so that the longest channel busy period is minimal is known to be NP-hard . The time complexity of proposed heuristic CSA is O(|X|log|X| + |X|M2) where |X| and M denote the number of successful requests in the CRI and the number of available channels respectively. Simulation results show that the proposed MAP protocol with CSA achieves an obviously higher throughput than conventional IEEE 802.11 WLAN with single channel.