Joint radar and communication (JRC) system is expected to significantly improve the utilization of spectrum resources, system performance, and reduce the equipment cost and size. In this letter, a JRC system containing a collocated multi-input multi-output (MIMO) radar and a multi-user communication base station is considered, which can serve several downlink users and detect multiple targets simultaneously. The radar signal covariance matrix and the communication physical precoder are jointly designed by matching the desired beampattern for radar detection while maximizing the downlink communication signal to interference and noise ratio (SINR). By relaxing the original problems, the iterative process with closed-form expressions is proposed to obtain the sub-optimal solutions of the system. Compared with solving the optimization problems directly, the proposed algorithm can significantly reduce the computational complexity with a little loss of system performance. Finally, simulation results show the effectiveness of the proposed algorithm.