Magnetic reconnection modulated by nonlocal disturbances in the solar atmosphere has been investigated theoretically, but rarely observed. In this study, employing H alpha and extreme ultraviolet (EUV) images and line-of-sight magnetograms, we report the acceleration of reconnection by an adjacent filament eruption. In H alpha images, four groups of chromospheric fibrils are observed to form a saddle-like structure. Among them, two groups of fibrils converge and reconnect. Two newly reconnected fibrils then form and retract away from the reconnection region. In EUV images, similar structures and evolution of coronal loops are identified. The current sheet forms repeatedly at the interface of reconnecting loops, with a width and length of 1-2 and 5.3-7.2 Mm and a reconnection rate of 0.18-0.3. It appears in the EUV low-temperature channels, with an average differential emission measure (DEM) weighed temperature and EM of 2 MK and 2.5 x 10(27) cm(-5). Plasmoids appear in the current sheet and propagate along it, and then further along the reconnection loops. The filament, located to the southeast of the reconnection region, erupts and pushes away the loops covering the reconnection region. Thereafter, the current sheet has a width and length of 2 and 3.5 Mm and a reconnection rate of 0.57. It becomes much brighter and appears in the EUV high-temperature channels, with an average DEM-weighed temperature and EM of 5.5 MK and 1.7 x 10(28) cm(-5). In the current sheet, more hotter plasmoids form. More thermal and kinetic energy is hence converted. These results suggest that the reconnection is significantly accelerated by the propagating disturbance caused by the nearby filament eruption.