Rotor stability is an important index of the performance of a magnetically levitated blood pump. In this study, we developed a novel nutation blood pump using a passive magnetic spherical bearing to achieve dynamic stability of a levitated rotor. The structure and working principle of the proposed blood pump are first introduced. A mathematical model based on the theory of equivalent magnetic charges is derived to calculate the axial and rotational stiffnesses of the passive magnetic spherical bearing. Furthermore, considering the gyro effect on the dynamic stability, an analytical expression for the gyroscopic moment of the nutating rotor is deduced. Finally, a prototype of a self-designed blood pump is fabricated, and a hydraulic experiment on the real-time levitation state is carried out. Experimental results obtained via different sensing components show that a continuous output flow rate of 5 L/min can be obtained against a pressure head of 100 mmHg at a rotational speed of 1600 rpm, and the output flow conditions are found to be stable at various pressures. In addition, it is found that the rotor becomes more stable with increasing rotational speed. The maximum fluctuation of the levitated gap is only 0.2 mm when the rotational speed of the rotor is 2300 rpm.