Abstract: The dynamic propertic of quasi-particles with different dispersion relations is investigated based on ultra-cold atomic gases in optical lattices. Numerical simulation of quasi-particle dynamics with and without the initial velocity is conducted by means of the numerical time-splitting spectrum and Heisenberg scenario analytic solution to equations of motion, and a thorough discussion is made on the effect of quasi-momentum power in dispersion relations on the dynamics of quasi-particles. The results show that relativistic Zitterbewegung(ZB) oscillation occurs in the system given that the quasi-momentum power in dispersion relations of the quasi-particles is an odd number. However, ZB does not occur in the process of quasi-particle dynamics with an even power. Besides, the greater the power of the quasi-momentum, the higher sensitivity of the quasi-particle drift to the initial velocity of the wave packets.