We have proposed a scheme of the generation and preservation of two-qubit steady-state quantum correlations through quantum channels where successive uses of the channels are correlated. Different types of noisy channels with memory, such as amplitude damping, phase-damping, and depolarizing channels have been taken into account. Some analytical or numerical results are presented. The effect of channels with memory on dynamics of quantum correlations has been discussed in detail. The results show that, steady-state entanglement between two initial qubits without entanglement subject to amplitude damping channel with memory can be generated. The entanglement creation is related to the memory coefficient of channel µ. The stronger the memory coefficient of channel µ is, the more the entanglement creation is, and the earlier the separable state becomes the entangled state. The result also shows that there exists nonlocality in the absence of entanglement. Besides, we compare the dynamics of entanglement with that of quantum discord when a two-qubit system is initially prepared in an entangled state. We show that entanglement dynamics suddenly disappears, while quantum discord displays only in the asymptotic limit. Furthermore, two-qubit quantum correlations can be preserved at a long time in the limit of µ → 1.