For the classical Cepheid U Sgr, we have constructed an O-C diagram spanning a time interval of 144 years. The O-C diagram has the shape of a parabola, which has made it possible to determine for the first time the quadratic light elements and to calculate the rate of evolutionary increase in the period, dP/dt=0.39(+/-0.10)s/yr, in agreement with the results of theoretical calculations for the third crossing of the instability strip. The available data reduced by the Eddington-Plakidis method reveal small random period fluctuations that do not distort the evolutionary trend in the O-C residuals.