Obtaining channel status information (CSI) is one of the main problems of the intelligent reflective surface (IRS) assisted communication system. This is because IRS has only a large number of passive reflective components and cannot process signals. In this paper, we aim to estimate downlink channel of IRS assisted multi-user multiple-input multiple-output (MU-MIMO) communication system. In time division duplex (TDD) mode, the downlink channel is estimated according to the uplink pilot by using channel reciprocity. We propose a parallel factor analysis based on projection subspace (PSS-PARAFAC) channel estimation scheme. In the first step, the common sparsity among multiple users is used for signal subspace projection to reduce noise energy and complexity. The second step is to convert each user signal received of base station (BS) into the PARAFAC problem. The iterative method of alternating least squares (ALS) is used to solve this problem. From the analysis of simulation results, the channel estimation performance of the proposed algorithm is better.