Mechanisms to provide QoS for IP communication have been frequently discussed recently. For example, in ITU-T and ETSI, the Next Generation Network has been discussed, and there are many reports on providing QoS for real-time services using RTP. However, in the current Internet, Transmission Control Protocol (TCP) is a major transport-layer protocol, and many real-time services are using TCP. In this paper, we present a performance evaluation of TCP under the control of a token bucket policer, which is one of the most common policing functions, and derive a formula of TCP throughput. We also evaluate the accuracy of our model by comparing results of simulations and experiments.