In this paper, joint transmit/receive frequency-domain equalization (FDE) is proposed for analog network coded (ANC) single-carrier (SC) bi-directional multi-antenna relay. In the proposed scheme, diversity transmission using transmit FDE is performed at relay station (RS) equipped with multiple antennas while receive FDE is carried out at base station (BS) and mobile terminal (MT) both equipped with single antenna. The transmit and receive FDE weights are jointly optimized so as to minimize the end-to-end mean square error (MSE). We evaluate, by computer simulation, the throughput performance and show that the joint transmit/receive FDE obtains the spatial and frequency diversity gains and accordingly achieve better throughput performance compared to either the transmit FDE only or the receive FDE only. It is also shown that ANC SC bi-directional multi-antenna relay can extend the communication coverage area for the given required throughput compared to conventional direct transmission.