In this paper, we study a transmit beamforming technique for multiple-input-multiple-output (MIMO) downlink multicast systems. Assuming that channel state information (CSI) is available at a transmitter, we try to maximize the lowest transmit data rate among users for a given transmit power level. Since finding the optimal beamforming vector requires prohibitively high computational complexity, we propose a reduced complexity scheme by applying greedy vector search and a simple power-allocation (PA) algorithm. Simulation results show that the proposed scheme outperforms the conventional semidefinite relaxation (SDR) technique and provides a performance quite close to the optimal performance with much reduced complexity.