The energy spectrum and the quantum entanglement in the Tavis-Cummings model are exactly solved, without the rotating wave approximation, and this exact solution of the energy spectrum is compared with the result under the rotating wave approximation. The influences of the atom state parameter θ and the atom-field coupling intensity at the initial time on the quantum entanglement are discussed. The results show that, when the coupling intensity is relatively weak, the energy spectrum under the rotating wave approximation is consistent with the exact solution. When the coupling intensity is relatively strong, there exist obvious differences between them. With the increase of θ, the entanglement degree increases gradually. With the increase of the coupling intensity, the phenomenon of entanglement sudden death between two atoms occurs. Moreover, the first occurrence time of entanglement sudden death becomes short and the duration of the entanglement death increases gradually.