The authors study quantum dynamics of a three-spin-qubit system with decoherence caused by its interactions with the environment in the Markov approximation. The obtained results are applied to study entanglement dynamics of the three-spin-qubit system which is initially prepared in GHZ or W states and transmitted through one of the decoherence channels. Applying the formula of the lower bound of concurrence for three-qubit the authors show that for the same decoherence channel, the W state, preserving more or less entanglement with the GHZ state, is dependent on the type of decoherence channel, the duration of decoherence and the physical properties of the channel. In particular, the calculations point out that quantum entanglement of the W state is preserved when passing through the phase flip channel, this channel created by a three-spin-qubit system interacting only with the common bath. In this case the entanglement of the W state is decoherence free entanglement.