We have carried out near-IR/optical observations to examine star formation toward a bright-rimmed cometary globule (BRC37) facing the exciting star(s) of an H ii region (IC1396) containing an IRAS source, which is considered to be an intermediate-mass protostar. With slitless spectroscopy we detected ten Hα emission stars around the globule, six of which are near the tip of the globule and are aligned along the direction to the exciting stars. There is evidence that this alignment was originally toward an O9.5 star, but has evolved to align toward a younger O6 star when that formed. Near-IR and optical photometry suggests that four of these six stars are low-mass young stellar objects (YSOs) with masses of ∼0.4 M . Their estimated ages of ∼1 Myr indicate that they were formed at the tip in advance of the formation of the IRAS source. Therefore, it is likely that sequential star formation has been taking place along the direction from the exciting stars toward the IRAS source, due to the UV impact of the exciting star(s). Interestingly, one faint, Hα emission star, which is the closest to the exciting star(s), seems to be a young brown dwarf that was formed by the UV impact in advance of the formation of other YSOs at the tip.