A computational study on the performance prediction of a two-stage axial compressor has been performed. A quasi-steady mixing-plane method is used on the rotor/stator interface to simulate the unsteady interaction phenomena. Detail flow mechanisms, for example, choke, stall, shock/boundary interaction, etc., have been observed and discussed in conjunction with performance characteristics. Calculational data agree reasonably well with the experimental data in terms of the performance characteristics showing the applicability of computational methods to the design validation of multistage axial compressors instead of experimental methods. But it is found that the stall margin of the original compressor was rather small, thus the design modification adopting a simple 1D/2D method has been conducted and its corresponding computations are also carried out. As a result of the redesign process, the stall margin becomes wide enough, but the overall performance is unsatisfactory, therefore, it seems that the redesign of the blades using 3-D methods is needed in the future work.