Entanglement decoherence of two particles interacting with the same environment is investigated by means of concurrence and the input-output fidelity. It is found that the entangled states of two-particle system can be divided into two kinds, coherence-preserving states and fragile entangled states. The dynamics of entanglement decoherence for fragile entangled states is discussed by taking into account the ohmic dissipation under the low temperature approximation.