TCP Vegas has the problem that it stops slow start too early, and it is more obvious in the large delay-bandwidth network. This phenomenon can cause a very long linear growth after entering congestion avoidance phase, and it will reduce the transmission efficiency. This paper analyzes that the reasons for this phenomenon is due to the exponential growth of slow start itself, then puts forward a dynamic growth algorithms of slow start, we call it Vegas-f. Improved algorithms can dynamically adjust the growth rate of slow start, so as to improve the transmission efficiency and competitiveness in mixing network. Simulation results show that the improved algorithm has completely solved the problem and the performance is improved significantly.