In this paper, the Tavis-Cummings(TC) model is generalized to simultaneously consider atomic motions and fields via intensity dependent coupling. Evolution of the fidelity of quantum states of entangled two-atom with motion interacting with light field via intensity-dependence coupling is investigated by means of the full quantum theory. The effects on the evolution of the fidelity of quantum states from the initial entanglement factor  of the two-atom and the average photon number n－ and field- mode structure parameter p of the field are researched by numerical calculations. The formation rule of quantum echoes of two-atoms is analyzed, and its physical essence is revealed. The results show that period quantum echo of the two-atom is always produced in the case of field-mode structure parameter p=1, independent of light intensity n－ and the initial entanglement factor  of the two-atom. Bell-state atoms can produce quantum echo with 2π/p cycle on the conditions of strongly coherent field, via changing the p of from 1 to any value less than 800. When p≥800, no matter what value of  takes，the light field is a vacuum field, weakly coherent field or strong coherent field, the fidelity of quantum states of the two- atom is always 1, that is the first class Bell state-atoms is in the fidelity state continuously. But when the initial entanglement factor  of two-atom is 3π/4, no matter how both values of n－, p are, the fidelity of quantum states of the two-atom maintains 1, namely the two-atom is in the fidelity state of the second class Bell-state continuously. The conclusions show that the extension model has good properties of periodic quantum echoes of two-atom, and provides the theoretical parameters and physical carrier for high fidelity output of entangled two-atoms information and experimental implementation of quantum information processing in the noise environment.