In this paper, optimal linear transceiver designs for multi-hop amplify-and-forward (AF) Multiple-input Multiple-out (MIMO) relaying systems with Gaussian distributed channel estimation errors are investigated. Some commonly used transceiver design criteria are unified into a single matrix-variate optimization problem. With novel applications of majorization theory and properties of matrix-variate function, the optimal structure of robust transceiver is first derived. Based on the optimal structure, the original transceiver design problems are reduced to much simpler problems with only scalar variables whose solutions are readily obtained by iterative water-filling algorithms. The performance advantages of the proposed robust designs are demonstrated by the simulation results. © 2011 IEEE.