We investigated the dissipative dynamics of quantum discord for correlated qubits underMarkovian environments. The basic idea in the present scheme is that quantum discord is more general,and possibly more robust and fundamental, than entanglement.We provide three initially correlated qubitsin pure Greenberger-Horne-Zeilinger (GHZ) or W state and analyse the time evolution of the quantumdiscord under various dissipative channels such as: Pauli channels σx, σy, and σz, as well as depolarisingchannels. Surprisingly, we find that under the action of Pauli channel σx, the quantum discord of GHZstate is not affected by decoherence. For the remaining dissipative channels, the W state is more robustthan the GHZ state against decoherence. Moreover, we compare the dynamics of entanglement with thatof the quantum discord under the conditions in which disentanglement occurs and show that quantumdiscord is more robust than entanglement except for phase flip coupling of the three-qubits system to theenvironment.