Abstract: The combined Block Diagonalization (BD) and geometric mean decomposition (BD-GMD) is a precoding scheme that is asymptotically optimal for (moderately) high signal-to-noise ratio (SNR) in terms of both channel throughput and the symbol error rate (SER) performance in downlink multi-user multiple-input-multiple-output (MU-MIMO) systems. The number of simultaneously supportable users with BD-GMD is limited by the number of transmit and receive antennas. In a downlink MU-MIMO system with a large number of users, the basestation may select a subset of users to serve in order to maximize the total throughput. The brute-force search for the optimal user set, however, is computationally prohibitive. We propose a low complexity suboptimal user selection algorithm for downlink MU-MIMO systems with BD-GMD. We show that the proposed algorithm have linear complexity in the number of users and achieve around 95% of the total throughput of the complete search method in simulations.