A newly designed magnetically suspended axial blood pump is presented, in which a 5 degrees-of-freedom rotor is suspended by using two conical active magnetic bearings, each with a four-pole stator. The preferred configuration could provide a rather large moment of inertia to increase the rotating stability of the suspended rotor in the pump. The hydrodynamic performance and internal flow fields in the pump are investigated by computational fluid dynamics. The pump head flow characteristics and the efficiency-Q curves at various rotating speeds are obtained, and the detailed flow fields in the pump are determined numerically. The distribution of shear stress, including Reynolds shear stress, is studied and discussed. Also, special attention is given to the small clearance between the rotor and the pump shell where the reversed secondary flow is formed and can flush out the clearance to avoid the flow stagnations. The secondary flow as well as the magnetic bearings can reduce thrombus in the pump. To check the biocompatibility of the pump further, the hemolysis indexes of the pump are estimated on the basis of the computed results.