A light bridge is a prominent structure commonly observed within a sunspot. Its presence usually triggers a wealth of dynamics in a sunspot and has a lasting impact on sunspot evolution. However, the fundamental structure of light bridges is still not well understood. In this study, we used the high-resolution spectropolarimetry data obtained by the Solar Optical Telescope on board the Hinode satellite to analyze the magnetic and thermal structure of a light bridge at AR 12838. We also combined the high-cadence 1700 angstrom channel data provided by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the dynamics on this bridge. We found a pair of blue and red Doppler shift patches at two ends of this bridge; this pattern appears to be the convective motion directed by the horizontal component of the magnetic field aligned with the spine of the bridge. Paired upward and downward motions imply that the light bridge could have a two-legged or undulating magnetic field. Significant 4 minute oscillations in the emission intensity of the 1700 angstrom bandpass were detected at two ends, which overlapped the paired blue- and redshift patches. The oscillatory signals at the light bridge and the penumbra were highly correlated with each other. Although they are separated in space at the photosphere, the periodicity seems to have a common origin from underneath the sunspot. Therefore, we infer that the light bridge and penumbra could share a common magnetic source and become fragmented at the photosphere by magnetoconvection.