Geometric quantum discord is a measure of quantum correlations. Combining quantum entanglement and geometric quantum discord, the comparison of quantum correlations of two-qubits initially in X-state was investigated in non-Markovian process by using analytical and numerical methods. The results show that in some initial states, both the concurrence and geometric quantum discord decay because of existence of the dissipation environments. However, the geometric quantum discord damps more slowly than concurrence does, which shows that the survival time of geometric quantum discord is longer than that of the entanglement. In other words, geometric quantum discord is more robust than entanglement to against the relaxation processes. Therefore, the quantum correlation is also a useful resource to realize quantum information processing.