The tip clearance has an important effect on the performance of an engine compressor. While the impact of tip clearance on a concentric compressor has been widely explored in previous research, the flow field distribution of an eccentric compressor has only been minimally explored. Both the steady and unsteady computational fluid dynamics (CFD) methods have been widely used in the studies of concentric axial-compressors, and they have similar simulation results in terms of flow field. However, they have been rarely applied to axial-compressors with non-uniform tip clearance to investigate their flow field. In this paper, ANSYS CFX is used as CFD software, and both steady and unsteady CFD methods are applied to study a single rotor of ROTOR67 to investigate the compressor characteristic line and flow field under different eccentricity conditions. The results show that non-uniform tip clearance creates a non-uniform flow field at the inlet and tip regions over the whole operating range. The circumferential position where the flow coefficient and the axial velocity are the smallest occurs at a position close to the maximum tip clearance and is located on the side deviating toward the direction of rotation of the rotor. Compared with steady CFD, unsteady CFD has better predictive capability for the flow field distribution in axial compressors with non-uniform tip clearance.