A novel semi-blind channel estimation is devised to jointly estimate the channel matrices of all links in a three-hop multiple-input multiple-output (MIMO) relay system. By exploiting the KRST coding structure in the source node, a PARAFAC tensor model is firstly investigated in the process of estimating the compound channel matrix consisting the channel state information of all links. Then, through the designed of amplification matrices at relay nodes, a PARATUCK-2 tensor based algorithm is further designed to extract all the sub-channel matrices. The proposed algorithm uses a two-stage iterative fitting algorithm for joint symbols and channels estimation. The uniqueness issue of proposed algorithm is well studied. Moreover, compared to existing methods, the proposed algorithm can avoid error propagation by making full use of the uniqueness characteristic of tensor operator as well as improve the spectral efficiency with few pilots. Numerical examples demonstrate the effectiveness of the proposed algorithm.