This paper presents a negative refractive index tunable metamaterial based on F-Shape structure which is capable of achieving dual-band negative permeability and permittivity, thus dual-band negative refractive index. An electromagnetic simulation was performed and effective media parameters were retrieved. Numerical investigations show clear existence of two frequency bands in which permeability and permittivity both are negative. The two negative refractive index bandwidths are from 23.8 GHz to 24.1 GHz and from 28.3 GHz to 34.9 GHz, respectively. The geometry of the structure is simple so it can easily be fabricated. The proposed structure can be used in multiband and broad band devices, as the band range in second negative refractive index region is 7 GHz, for potential applications instead of using complex geometric structures and easily tuned by varying the separation between the horizontal wires.