Cavitation instabilities such as rotating cavitation and cavitation surge often occur in high speed turbopumps. In the present study, numerical simulation of cavitation surge, which numerically solves the one-dimensional momentum and continuity equations with modelled dynamic cavitation characteristics, is conducted. The phase lag of cavity response against the inlet pressure and the suction flow rate variations is modeled in the form of the first-order lag system considering that the frequency of cavitation surge is small. Differently from linear stability analysis made in our previous study, the equations are solved in time domain with retaining some of non-linear terms. The method is validated through the comparison with the stability analysis. Then the effect of phase lags in dynamic cavitation characteristics is examined.