In this paper, we consider a relay system in multipleinput multiple-output (MIMO) multi-user channels where a single MIMO relay is engaged in communication between multiple source-destination terminal pairs. We propose two amplify-and-forward (AF) relaying schemes which maximize the sum-rate for the interference channel with multiple source-destinations. First, we introduce an iterative scheme which provides a local optimal solution. The proposed scheme iteratively searches an optimum relay matrix by deriving the gradient of the sum-rate and applying the gradient descent algorithm. Next, in order to reduce the computational complexity of the iterative scheme, we propose a block diagonalization (BD) method which utilizes the minimum mean-square error (MMSE) criterion with singular value decomposition (SVD) based rate maximization. Simulation results show that the proposed iterative scheme achieves a nearoptimal sum-rate for the given channel model, and the MMSE based BD with the rate maximization approaches the local optimal sum-rate at high signal-to-noise ratio (SNR) regime.