The master equation of density matrix in the interaction system of atom with thermal reservoir can be solved by virtue of the Ket-Bra entangled state method and the analytical solution expression is shown. Atomic dipole squeezing effect in this system is numerically studied and the effects of the mean number of photons in the thermal reservoir and the atomic spontaneous emission rate on the atomic dipole squeezing effect are discussed. The results show that the atomic dipole squeezing effect is weakened with the increase of the mean number of photons and the atomic spontaneous emission rate.