We present dynamic tuning of optical resonance using microelectromechanical systems (MEMS)-driven coupled photonic crystal (PhC) nanocavities. The device consists of an air-suspended one-dimensional PhC nanocavity coupled to input and output waveguides and a perturbing nanocavity attached to a submicrometer MEMS comb drive. Resonance tuning is achieved through varying the gap between the two coupled cavities. We demonstrate experimentally that resonance can be tuned up to 8nm with no significant deterioration in the Q factor. The proposed mechanism potentially enables a new platform of on-chip photonic devices that can achieve a large tuning range with low power and small footprint and may find useful applications in tunable optical/photonic devices.