Future wireless Internet services require a broadband frequency spectrum with high data rates. Cognitive radio (CR) concept is a novel approach to improve the spectrum efficiency. The CR is based on the opportunistic usage of frequency spectrum, which is not occupied by the primary users. Conventional multi-user access in bi-directional CR network may be done by using either time division multiple access (TDMA), frequency division multiple access (FDMA) or code division multiple access (CDMA). Without adaptive or dynamic frequency reuse, TDMA and FDMA have lower spectrum efficiency in comparison with CDMA. However, the problem of CDMA in a multipath channel is a multi-user interference (MUI). In this paper, we present a bi-directional CR network with wireless network coding (WNC) in a multipath channel. Unlike the conventional multi-user bi-directional CR network, where the users access the spectrum holes in different time-slot or frequency, the proposed method allows secondary users (SUs) to access the spectrum holes simultaneously. The performance of bi-directional CR network with WNC is theoretically analyzed in terms of spectrum efficiency and the maximum number of SUs. The numerical results show that the spectrum efficiency and the maximum number of SUs of the proposed method increases in comparison with conventional CR network.