  We evaluate analytically the quantum discord for a large family of multi
qubit states. It is interesting to note that the quantum discord of three
qubits and five qubits is the same, as is the quantum discord of two qubits and
six qubits. We discover that the quantum discord of this family states can be
concluded into three categories. The level surfaces of the quantum discord in
the three categories is shown through images. Furthermore, we investigated the
dynamic behavior of quantum discord under decoherence. For the odd partite
systems, we prove the frozen phenomenon of quantum discord does not exist under
the phase flip channel, while it can be found in the even partite systems.
