not-yet-known not-yet-known not-yet-known unknown Optimum performance of co-existing radar and communication (CRC) system is a challenging task when target and user exist within a crowded area where path-loss is dominant. Inspired by the application of intelligent reflecting surface (IRS) in reconstructing the wireless transmission environment, this paper investigates deploying IRS to the CRC system to pursue performance improvement. Particularly, we consider an IRS-assisted CRC system where the IRS not only provides an indirect communication path but inevitably introduces additional interfering paths. Our goal is to maximize the radar signal-to-interference-plus noise ratio (SINR) by jointly optimizing the transmit beamform and the phase of IRS while satisfying the user SINR, the total transmit power at the radar and base station (BS), the restriction of IRS phaseshift. An efficient alternative optimization algorithm combining the second-order cone programming (SOCP) and semidefinite programming (SDP) optimization methods is exploited to solve the complicated non-convex unit-norm problem. Simulation results reveal the advantages of deploying IRS in the CRC system and the effectiveness of our proposed algorithm.