This paper proposes an improvement to the TCP ramp up behavior in slow-start. Current implementations of the TCP start-up procedure may result in an exponential growth of the congestion window, which results in the transmission of an excessive number of packets. Consequently, the network becomes congested and the self-clocking mechanism of the TCP fails. By estimating the number of packets that which can be in flight in the network from the viewpoint of the TCP source, this study develops an algorithm to suppress congestion before it becomes significant. The simulation results indicate that the proposed algorithm enhances the TCP performance by establishing a smoother transmission rate at the end of the slow-start phase and reducing the number of dropped packets significantly as a result.