This paper reports the results of lattice Boltzmann simulations of the rotation behaviour of neutrally buoyant spheroidal particles in a three-dimensional Couette flow. We find several distinctive states depending on the Reynolds number range and particle shape. As the Reynolds number increases, rotation may change from one state to another. For a prolate spheroid, two rotation transitions are found. In the low Reynolds number range $0<R<R_1\approx 205$, the prolate spheroid rotates around its minor axis, which is parallel to the vorticity vector of the flow. The rate of rotation is a periodic function of time. In the intermediate Reynolds number range $R_1 < R < R_2\approx 345$, the prolate spheroid precesses about the vorticity direction with a nutational motion. The angular velocities are periodic functions of time. The mean nutation angle between the major axis and the vorticity increases monotonically as the Reynolds number increases. In the high Reynolds number range $R_2 < R < 467$, the prolate spheroid rotates with a constant rate around its major axis, which is parallel to the vorticity. For an oblate spheroid, only one rotation transition is observed. In the lower Reynolds number range $0 < R < R_1' \approx 220$, the oblate spheroid finally spins with a constant rate around its minor axis (the symmetric axis of the revolution), which is parallel to the vorticity vector. In the higher Reynolds number range $220 \approx R_1' < R < 467$, the oblate spheroid still spins with a constant rate around its minor axis but there is a finite inclination angle between the minor axis and the vorticity vector. This angle increases as the Reynolds number increases.