In this study, the authors present a novel channel estimation algorithm for three-hop multi-input multi-output (MIMO) relay systems using the PARATUCK2 tensor model. At the destination, the proposed algorithm exploits a unified formulation of the received signal as a PARATUCK2 model, and jointly estimates all of the channel matrices involved in the communication. Compared with existing algorithms, the proposed algorithm only requires the source to transmit the channel training sequences, does not need relays to perform any task of channel estimation, and yields smaller estimation error. Moreover, the proposed algorithm can be extended to multi-hop MIMO relay systems with any number of hops. Numerical examples are shown to demonstrate the effectiveness of the PARATUCK2-based channel estimation algorithm.