With immersed boundary-lattice Boltzmann method, inertial migration behavior and rotational dynamics of an ellipsoidal particle in an infinite square cross-section microchannel were numerically studied. Two main motion states were found for ellipsoidal particles migrating in a microchannel, i.e., tumbling and log-rolling. It shows that for particles in flow with relatively low Re (Re=10), rotational behavior varied from different initial orientation. However, for particles in flow with higher Re (50≤Re≤200), they perform same rotational behavior and reach the same equilibrium position. As Re number increases, equilibrium position of the ellipsoidal particle moves firstly towards the wall then the center of the channel. At higher Re numbers (Re>300), the particles do not retain stable inertial focusing. Finally, the phenomena were analyzed from flow field around the particles. In addition, mechanism of transition of motion states of particles is explained from fluid and particle inertia.