The entanglement dynamics of two interacting qubits under the influence of Markovian environment and non-Markovian environment was examined by making use of the linear entropy. The effect of the strength of the dipole-dipole interaction and the detuning between the transition frequency of the atom and the center frequency of the reservoir on the time evolution of entanglement was discussed. It is shown that linear entropy decreases with the increase of the strength of the dipole-dipole interaction and the detuning between the transition frequency of the atom and the center frequency of the reservoir. Linear entropy tends to steady state within a short time in the Markovian environment, but in the non-Markovian environment linear entropy shows oscillatory behavior with the time evolution.