It is unclear whether successive filament eruptions at different sites within a short time interval are physically connected or not. Here, we present the observations of successive eruptions of a small and a large filament in a tripolar magnetic field region whose coronal magnetic field showed as a fan-spine magnetic system. By analyzing the multiwavelength observations taken by the Solar Dynamic Observatory and the extrapolated three-dimensional coronal magnetic field, we find that the two filaments resided respectively in the two lobes that make up the inner fan structure of the fan-spine magnetic system. In addition, a small fan-spine system was also revealed by the squashing factor Q map, which located in the east lobe of the fan structure of the large fan-spine system. The eruption of the small filament was a failed filament eruption, which did not cause any coronal mass ejection (CME) except for three flare ribbons and two post-flare-loop systems connecting the three magnetic polarities. The eruption of the large filament not only caused similar post-flare-loop systems and flare ribbons, as observed in the small filament eruption, but also a large-scale CME. Based on our analysis results, we conclude that the two successive filament eruptions were physically connected, in which the topology change caused by the small filament eruption is thought to be the physical linkage. In addition, the eruption of the small fan-spine structure further accelerated the instability and violent eruption of the large filament.