We prove that TCP Vegas globally converges to its equilibrium point in finite time assuming no feedback information delay. We analyze a continuous-time TCP Vegas model with discontinuity and high nonlinearity. Using the upper right-hand derivative and applying the comparison lemma, we cope with the discontinuous signum function in the TCP Vegas model; using a change of state variables, we deal with the high nonlinearity. Although we ignore feedback information delay in analyzing the model of TCP Vegas, the simulation results illustrate that TCP Vegas in the presence of feedback information delay shows very similar dynamic trends to TCP Vegas without feedback information delay. Consequently, dynamic properties of TCP Vegas without feedback information delay can be used to estimate those of TCP Vegas in the presence of feedback information delay.