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Coordinated Multi-Point Transmission and Reception (CoMP) has been regarded as an important component for Long Term Evolution-Advanced (LTE-A) which is currently standardized in the Third Generation Partnership Project (3GPP). CoMP is mainly expected to increase cell-edge User Equipment (UE) throughput and/or system throughput. In order to reach the desired performance, uplink power control is a key point since it is typically used to acquire the desired received SINR of eNodeB while limiting the generated inter-cell interference. In this paper we propose an improved uplink power control method for CoMP system that adjusts the parameters in the uplink power control formula of LTE system to improve cell-edge throughput and reduce the UE transmit power with almost no reduction of the system throughput. The method is only suitable for CoMP uplink Joint Reception (JR) scenario. The comparison is carried out in terms of average and outage system throughput and UE average transmit power through the system simulation.