Quantum discord(QD) can be used to characterize quantum correlation of a quantum system. Based on geometric measurement of QD(GMQD), quantum correlation of the single-parameter X- state was calculated, and the results for the case were also given under three different quantum channels. For the amplitude-damping channel, by comparing concurrence and GMQD of the X-state mentioned above using graphical method, it’s concluded that GMQD exhibits more robust than concurrence when the quantum system is exposed to environment.