We analyze the deep Chandra data of the nearby IC 1262 group, and find that the bow-shaped structure, located about 17 kpc (25″) east of the X-ray peak, is a cold front moving eastward with a Mach number of M = 0.7± 0.1. Furthermore, the line-of-sight velocity distribution of the member galaxies is clearly divided into two subgroups. Assuming the same mass-to-light ratio, the group is undergoing a major merger. Since the cooler core of the group as a whole is not destroyed by the merger, and the high-velocity subgroup has a component of eastward movement, it can be naturally explained that the cold front appears on the east side of the group center.