Dynamical jets are generally found on light bridges (LBs), which are key to studying sunspot decay. So far, their formation mechanism is not fully understood. In this paper, we used state-of-the-art observations from the Goode Solar Telescope, the Interface Region Imaging Spectrograph, the Spectro-polarimeter on board Hinode, and the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory to analyze the fan-shaped jets on LBs in detail. A continuous upward motion of the jets in the ascending phase is found from the H alpha velocity that lasts for 12 minutes and is associated with the H alpha line wing enhancements. Two mini jets appear on the bright fronts of the fan-shaped jets visible in the AIA 171 and 193 angstrom channels, with a time interval as short as 1 minute. Two kinds of small-scale convective motions are identified in the photospheric images, along with the H alpha line wing enhancements. One seems to be associated with the formation of a new convection cell, and the other manifests as the motion of a dark lane passing through the convection cell. The finding of three-lobe Stokes V profiles and their inversion with the NICOLE code indicate that there are magnetic field lines with opposite polarities in LBs. From the H alpha - 0.8 angstrom images, we found ribbon-like brightenings propagating along the LBs, possibly indicating slipping reconnection. Our observation supports the idea that the fan-shaped jets under study are caused by magnetic reconnection, and photospheric convective motions play an important role in triggering the magnetic reconnection.