For a blood pump, the blood flow channel and impeller parameters directly affect the performance of the pump and the resulting blood circulation. The flow channel in particular has a great impact on the hydraulic performance of the pump (e.g., flow and pressure), which directly determines the overall performance of the blood pump. Traditional bearing-supported blood pumps can cause mechanical damage to blood cells, leading to hemolysis and thrombosis. In this study, therefore, we designed a conical spiral axial blood pump with magnetic levitation. The blood pump was supported by electrodynamic bearings in the radial direction and electromagnetic bearings in the axial direction. The impeller and the front and rear hubs were integrated to minimize blood stagnation and reduce the formation of thrombosis. The hub had a conical spiral flow channel design, which not only reduced the size of the impeller but also increased blood flow and pressure while meeting the design requirements. Computational fluid dynamics (CFD) analysis was used to analyze the flow field of the axial blood pump, a power function model was used to establish a hemolysis prediction model, and the particle tracking method was used to obtain the flow trajectories of individual blood cells, thereby predicting hemolysis-related performance of the blood pump. The simulation results showed that the main high shear stress area in the blood pump was located in the impeller inlet and the clearance between the top of the impeller and the inner chamber of the blood pump. When the hub taper angle of the blood pump was 0.72° and the clearance was 0.3 mm, the average hemolysis prediction value was 0.00216. This prediction value was smaller than that of traditional axial blood pumps. These findings can provide an important reference for the structural design of axial blood pumps and for reducing the hemolysis prediction value.