Under potential flow assumption, a numerical method is established to simulate the nonlinear movement of the free surface after the breakup of a bubble, with taking the surface tension and viscous into consideration. A method to handle the splitting of the jet or drop is put forward. Besides, an experiment of rising bubble bursting at the free surface is conducted, and the numerical result is in good agreement with the experimental result. In order to study the mechanism and law of the free surface movement after bubble breakup, the dynamic behavior of different sizes of bubble breakup is studied with the program developed, including the jet from the bottom of the bubble, the splitting of the jet or drop and so on. The variation law of the size and time of the first splitting drop, and the maximum velocity of the jet is studied and summarized. Finally, the influences of Reynolds number and Weber number on the free surface after bubble breakup are also analyzed.