The concurrence of the two atoms with dipole-dipole interaction in the Tavis-Cummings model in an initial х state is derived. The influence of the dipole-dipole interaction on the entanglement time evolution and the entanglement sudden death (ESD) is analysed. The relation between the concurrence and the atomic interaction energy is investigated. The results show that the dipole-dipole interaction affects the concurrence and ESD remarkably, leads periods and amplitudes of the concurrence oscillation to change and time interval and number of the ESD to decrease. The relation between the concurrence and interaction energy relies on initial states of the atoms.