This research deals with nonlinear dynamics of a permanent magnet freely levitated above a high-Tc superconductor excited in the vertical direction, focusing on generation of spin torque acting on the magnet. Equations of 6 d.o.f. motion, nonlinearly coupled by magnetic force and torque, were described on the assumption that a magnet has an eccentricity between the center of gravity and the magnetic center. Force and torque were evaluated analytically by the flux frozen method. Dynamic behavior of the magnet was examined numerically for different frequencies of excitation. A simplified 2 d.o.f. system with only essential terms was introduced in order to discuss the mechanism of nonlinear coupling which generates spinning from vertical oscillation. Spinning motion of the magnet was examined in detail analytically by the method of harmonic balance. Experiments of vertical excitation were also carried out. Experimental results were compared with numerical ones.