The closed Brayton cycle operating with supercritical carbon dioxide is an attractive option for geothermal, nuclear and solar energy conversion. As one of the key component, the performance of the supercritical carbon dioxide compressor attracts lots of attention. Up to now, most studies focused on the centrifugal compressor and the design method of the axial compressor operating with supercritical carbon dioxide is far to matured. The effects of the tip clearance size on the tip leakage flow in an axial compressor are numerically investigated in the present work, with different tip clearance size and operating points. To fully take advantages of the matured design method of the air compressor, a similar air compressor is simulated as a comparison group. The results show that the flow characteristics especially the static pressure coefficient and tip leakage vortex structure is almost the same between S-CO2 compressor and the similar air compressor with small tip clearance size. This is also suitable for the large tip clearance size at low and middle span, while obvious discrepancy arises at high span. The tip leakage vortex of S-CO2 compressor is stronger and more downstream than the air compressor. Understanding these effects is helpful to extend the abundant experience of the air compressor to design S-CO2 compressor.