Ground-state cooling of mesoscopic mechanical objects is still a major challenge in the unresolved sideband regime. We present a frequency modulation (FM) scheme to achieve mechanical resonator cooling to its ground-state in a double-cavity optomechanical system containing a mechanical resonator. The mean phonon number is determined by numerically solving a set of differential equations derived from the quantum master equations. Due to efficient suppression of Stokes heating processes in the presence of FM, the ground-state cooling indicated by numerical calculations is achievable considerably no matter whether in the resolved sideband regime or the unresolved sideband regime. Furthermore, by choosing parameters reasonably, the improvement of the quantum cooling limit is found to be capable of being positively correlated with the modulation frequency. This method provides new insight into quantum manipulation and creates more possibilities for applications of quantum devices.