Although magnetic reconnection plays a key role in the formation of a solar filament, the detailed formation process is still ambiguous. Combining the observational data from the New Vacuum Solar Telescope and the Solar Dynamics Observatory, we analyzed the formation of a U-shaped filament via successive magnetic reconnection in the AR NOAA 11598 on 2012 October 25. The successive reconnection occurred between a filament (F) and its nearby chromospheric fibrils (CF). The associated brightening and magnetic cancellation were observed. The changes in appearance of the CF at the reconnection site were accompanied by the formation and accumulation of some new magnetic loops, as well as plasmas propagated along the formed magnetic loops from the reconnection site, indicating the changes in the topology of the F and CF. These can provide comprehensive observational evidence for successive reconnection. After the reconnection, a longer U-shaped filament was formed. During the formation of the U-shaped filament, two major magnetic energy releases took place. While in the two energy release processes, the injected plasma from the reconnection site can provide part of the material for the formation of the U-shaped filament. Therefore, we conclude that the successive reconnection results in both the dynamical evolution and the subsequent formation associated with the U-shaped filament. And the results of nonlinear force-free field extrapolation demonstrated that the magnetic topology of the F was changed significantly; this is consistent with the observational results and further confirms the formation of the U-shaped filament.