The paper describes a new admission control (AC) algorithm for greedy TCP connections. The algorithm has passed positive tests in preproduction QoS IP network [2], developed inside European IST project AQUILA1 network. The algorithm operates per single TCP flow and it assumes the setting of advertised receiver TCP window size for maintaining ideal TCP behaviour (no packet losses). The QoS objective is to guarantee the requested bit rate, say Rreq, a user demands from the network. Furthermore, on the basis of the Rreq and information about round trip time (RTT), the user request is mapped into the form of single token bucket parameters, i.e. token accumulating rate (R) and bucket size (BS), constituting input parameters for AC decision. For admitted TCP connection the Rreq is guaranteed, even if running connections differ in Rreq and RTTmin. Included simulation results confirm the efficiency of the algorithm.