A three-dimensional computation was conducted to understand effects of the inlet boundary layer thickness on the internal flow in a low-speed axial compressor operating at the design condition($phi=85\%$) and near stall condition($phi=65\%$). At the design condition, the flows in the axial compressor show, independent of the inlet boundary layer thickness, similar characteristics such as the pressure distribution, size of the hub comer-stall, tip leakage flow trajectory, limiting streamlines on the blade suction surface, etc. However, as the load is increased, the hub corner-stall grows to make a large separation region at the junction of the hub and suction surface for the inlet condition with thick boundary layers at the hub and casing. Moreover, the tip leakage flow is more vortical than that observed in case of the thin inlet boundary layer and has the critical point where the trajectory of the tip leakage flow is abruptly turned into the downstream. For the inlet condition with thin boundary layers, the hub corner-stall is diminished so it is indistinguishable from the wake. The tip leakage flow leans to the leading edge more than at the design condition but has no critical point. In addition to these, the severe reverse flow, induced by both boundary layer on the blade surface and the tip leakage flow, can be found to act as the blockage of flows near the casing, resulting in heavy loss.