This article reports the observation of the high-density front at the high field side (HFS) region in the limiter J-TEXT tokamak. In the J-TEXT high density discharges, the high-density front at the HFS scrape-off layer (SOL) region has been clearly identified by the far-infrared laser polarimeter-interferometer. The high-density front forms at the HFS SOL when the plasma density reaches a critical value, it can be up to seven times higher than the density in the low field side region and it stays stable as long as the density remains. In this stable phase, the local radiation is at a low level and it shares common characteristics with the high-field-side high-density (HFSHD) phenomena observed in divertor devices. If density increases continuously, the high-density front expands poloidally and evolves into an unstable 'moving' phase while propagating into the main plasma region, which eventually triggers the disruption. The maximum achievable density on J-TEXT seems to be correlated with the evolution of the high-density front, suggesting that the region may play a role in setting the operational limit on J-TEXT. The unstable phase of high-density front seems to share some common characteristics with the well-known multifaceted asymmetric radiation from the edge (MARFE), except that the radiation level in J-TEXT stays at a low level. The density threshold of the high-density front formation and the maximum density of the region itself increase with , consistent with the observation on both HFSHD and MARFE. The MARFE-like behavior of the high-density front in its final stage, suggests that MARFEs might be the result of these fronts forming in or moving into regions where the plasma temperature and impurity concentration are conducive for them to be radiatively unstable.