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Techniques for improving the network congestion have been proposed in different fields. In recent year, the congestion control problems were studied to enhance the routing performance for wireless sensor networks. In this paper, an adaptive NAV-assisted routing (ANAR) algorithm is proposed to improve the network congestion with a cross- layer approach. The NAV vectors obtained from the RTS/CTS packets are utilized for the determination of the channel status around a sensor node. The routing path is selected based on the congestion-free probability along the route for the transmission of data packets. Moreover, the adaptive path- switching scheme further enhances the routing performance of the proposed ANAR algorithm. The effectiveness of the ANAR protocol is illustrated via the simulations. Without consuming excessive power for each sensor node, the ANAR algorithm can achieve better performance comparing with other existing schemes, especially under the scenarios with network congestion.