Transmission of TM-polarized light through a subwavelength metal-dielectric grating structure exhibits strong resonance in the visible range. Simulations by finite-difference time-domain and finite-element methods show that the resonance can be attributed to the magnetic response. Further simulation shows that the grating structure can be optimized by adding an index matching dielectric layer to produce negative refractive index response in the visible band. Easily fabricated using nanoimprint lithography and conveniently able to be excited by incident light normal to the fabrication plane, such metal-dielectric grating structure could find potential use in large area negative refractive index applications.