An all-dielectric fishnet metamaterial (DFM) composed of multilayer dielectric structure with periodically patterned holes is proposed to generate left-handed behavior in optical frequency region. Different from the metallic fishnet negative index metamaterial realized by coupling the neighbouring functional layers along the propagation direction, this DFM owes its simultaneous negative permeability and permittivity to the hybrid coupled resonances in the same layer. Based on this configration, a wide-band and polarization-independent negative refraction with maximum figure of merit as large as 13.85 is obtained by a silicon-based DFM at 450 nm wavelength. Simple and easy to fabricate, this concept is believed to provide an alternative route to realize high-performance negative index metamateirals at optical frequencies.