In the unresolved sideband regime,we propose a scheme for cooling mechanical resonator close to its ground state in a three-cavity optomechanical system,where the auxiliary cavities are indirectly connected with the mechanical resonator through standard optomechanical subsystem.The standard optomechanical subsystem is driven by a strong pump laser field.With the help of the auxiliary cavities,the heating process is suppressed and the cooling process of the mechanical resonator is enhanced.More importantly,the average phonon number is much less than 1 in a larger range.This means that the mechanical resonator can be cooled down to its ground state.All these interesting features will significantly promote the physical realization of quantum effects in multi-cavity optomechanical systems.