HD106906b is an \sim 11 M _ { \mathrm { Jup } } , \sim 15 Myr old directly-imaged exoplanet orbiting at an extremely large distance from its host star . The wide separation ( 7.11 \arcsec ) between HD106906b and its host star greatly reduces the difficulty in direct-imaging observations , making it one of the most favorable directly-imaged exoplanets for detailed characterization . In this paper , we present HST/WFC3/IR time-resolved observations of HD106906b in the F127M , F139M , and F153M bands . We have achieved \sim 1 \% precision in the lightcurves in all three bands . The F127M lightcurve demonstrates marginally-detectable ( \edit 1 2.7 \sigma significance ) variability with a best-fitting period of 4 hr , while the lightcurves in the other two bands are consistent with flat lines . We construct primary-subtracted deep images and use these images to exclude additional companions to HD106906 that are more massive than 4 M _ { \mathrm { Jup } } and locate at projected distances of more than \sim 500 au . We measure the astrometry of HD106906b in two HST/WFC3 epochs and achieve precisions better than 2.5 mas . The position angle and separation measurements do not deviate from those in the 2004 HST/ACS/HRC images for more than 1 \sigma uncertainty . We provide the HST/WFC3 astrometric results for 25 background stars that can be used as reference sources in future precision astrometry studies . Our observations also provide the first 1.4- \micron water band photometric measurement for HD106906b . HD106906b ’ s spectral energy distribution and the best-fitting BT-Settl model have an inconsistency in the 1.4- \micron water absorption band , which highlights the challenges in modeling atmospheres of young planetary-mass objects .