The paper investigates closed-loop spatial multiplexing systems with transmit antenna selection. Since the bandwidth limit of feedback channel, a partial MRT algorithm is proposed to reduce the amount of feedback information. An improved water-filling power allocation algorithm is obtained for optimal power allocation. The proposed method can not only reduce the amount of feedback, but also fully exploit potential multiplexing capability of the channel. Simulation results show that transmit antenna selection can compensate the loss caused by imperfect CSI at the transmitter.