We present a cooling mechanism for a nanomechanical resonator that linearly couples with a LC oscillator. The linear coupling, when periodically modulated at red detuning, up-converts the low-frequency nanomechanical quanta to the high-frequency LC oscillator quanta which then dissipates in the circuits via the damping of the LC oscillator. We show that realistic circuit can be designed in the superconducting system to implement this scheme in the resolved-sideband regime and reach the quantum ground state of the nanomechanical mode. A detailed study of the origin of the quantum back-action noise in this cooling process is also presented.