The entanglement time evolution of Tavis-Cummings model with Gaussian coupling is investigated. The entanglement between coherent field and two atoms is explored by using the quantum reduced entropy,and the entanglement between two atoms is studied by using Negativity entropy. Using the numerical method,the influences of the atomic motion perpendicularity to the axes of resonant cavity and initial states of the system on the entanglement are discussed. The results indicate that the time evolutions of the two entanglements are similar. But at the same time the stronger the entanglement between field and two atoms is,the weaker that between the two atoms is. The motion affects the entanglement. When the mean photon number increases,the Rabi frequency increases while the vibration amplitude decreases. When the atomic initial state changes,the entanglement appears similar time evolution.