Magnetic reconnection, the rearrangement of magnetic field topology, is a fundamental physical process in magnetized plasma systems all over the universe1,2. Its process is difficult to be directly observed. Coronal structures, such as coronal loops and filament spines, often sketch the magnetic field geometry and its changes in the solar corona3. Here we show a highly suggestive observation of magnetic reconnection between an erupting solar filament and its nearby coronal loops, resulting in changes in connection of the filament. X-type structures form when the erupting filament encounters the loops. The filament becomes straight, and bright current sheets form at the interfaces with the loops. Many plasmoids appear in these current sheets and propagate bi-directionally. The filament disconnects from the current sheets, which gradually disperse and disappear, reconnects to the loops, and becomes redirected to the loop footpoints. This evolution of the filament and the loops suggests successive magnetic reconnection predicted by theories1 but rarely detected with such clarity in observations. Our results on the formation, evolution, and disappearance of current sheets, confirm three-dimensional magnetic reconnection theory and have implications for the evolution of dissipation regions and the release of magnetic energy for reconnection in many magnetized plasma systems.