We present new high-resolution ($sim$0farcs09) $H$-band imaging observations of the circumstellar disk around the T Tauri star SU Aur. Our observations with Subaru-HiCIAO have revealed the presence of scattered light as close as 0farcs15 ($sim$20 AU) to the star. Within our image, we identify bright emission associated with a disk with a minimum radius of $sim$90 AU, an inclination of $sim$35degr from the plane of the sky, and an approximate P.A. of 15degr for the major axis. We find a brightness asymmetry between the northern and southern sides of the disk due to a non-axisymmetric disk structure. We also identify a pair of asymmetric tail structures extending east and west from the disk. The western tail extends at least 2farcs5 (350 AU) from the star, and is probably associated with a reflection nebula previously observed at optical and near-IR wavelengths. The eastern tail extends at least 1arcsec (140 AU) at the present signal-to-noise. These tails are likely due to an encounter with an unseen brown dwarf, but our results do not exclude the explanation that these tails are outflow cavities or jets.