In order to study the design method of high performance compact pump, a high specific speed mixed-flow pump was designed with axial pump configuration by solving the 3-D inverse design equations and the full viscid flow iteratively. Firstly, the performance of the high specific speed mixed-flow pump was calculated using RANS simulation, the results of CFD simulation and test data were presented and discussed briefly. The errors of the mixed-flow pump power between the CFD simulation and pump test data were below 3% in the whole calculating region. Secondly, based on the axial pump configuration, the pump was redesigned by using 3-D inverse design method and CFD simulation iteratively. The final design result indicated that the pump had high efficiency of 0.927 on the design point and the flow within the pump was smooth without any separation and cavitation. In the end, the performance of the mixed-flow pump and the redesigned compact pump were compared, which indicated that the efficiency of the redesigned compact pump was higher than the mixed flow pump by 3%, and the transom size of the redesigned compact pump was smaller than the mixed-flow pump by 38%. The redesigned pump had compact size and excellent performance.