  We propose to cool a mechanical resonator close to its ground state via an
electromagnetically-induced-transparency- (EIT-) like cooling mechanism in a
double-cavity optomechanical system, where an additional cavity couples to the
original one in the standard optomechanical system. By choosing optimal
parameters such that the cooling process of the mechanical resonator
corresponds to the maximum value of the optical fluctuation spectrum and the
heating process to the minimum one, the mechanical resonator can be cooled with
the final mean phonon number less than that at the absence of the additional
cavity. And we show the mechanical resonator may be cooled close to its ground
state via such an EIT-like cooling mechanism even when the original resolved
sideband condition is not fulfilled at the absence of the additional cavity.
