A quantum system for the interaction of a two-mode coherent state field with V-type atom have been studied. The population and quantum entanglement of quantum systems were solved accurately without rotating-wave approximation. The effects of average photon number n- and atomic level superposition on the population and quantum entanglement were discussed, and the reasons of the non-rotational-wave terms transition affecting the dynamics of quantum systems were analyzed. The results show that the population and quantum entanglement evolution period increase with the increase of n-. The entanglement degree of the quantum system is smaller in the population collapse region and larger in the population recovery region. The initial value of quantum entanglement and the mean value decreases when the atom is in the superposition state at the initial time. The non-rotating-wave terms transition leads to a zigzag oscillation in the population and entanglement evolution curves.