Ground-state cooling of the mechanical degree of freedom is a fundamental requirement for quantum state transfer between relevant optical and mechanical systems. Here, we fabricate optomechanical crystal cavities with co-localized mechanical and optical modes on a monolithic chip. The typical linewidth of the optical modes at telecom wavelength is as low as 0.95 GHz, and the mechanical resonant frequency is around 5 GHz, which means the optomechanical system can be operated in the resolved sideband regime. With the statistics of the asymmetry in the scattering rates of red and blue detuning driving processes, we initialize and characterize the mechanical system in its quantum ground-state of motion, with a mean thermal phonon occupancy n¯th=0.018±0.0034, corresponding to amode temperature of 57.3 mK. It is a general platform for quantum state transfer between relevant optical and mechanical systems, as well as the quantum entanglement between these systems.