The electronic properties of silicon nanoribbons (SiNRs) with strain are studied by ab initio and tight-binding calculations. The strain modulated band gap variations of NANA-ASiNRs depend on the family types categorized according to NA = 3p, 3p + 1 and 3p + 2 and could be tuned over several hundreds meV. For (3p + 2)-ASiNRs, the band gaps are proved to be linear as a function of strains and exactly closed under small tensile strains. Meanwhile, the structure of the lowest conduction and highest valence bands are Dirac-type dispersion. These results suggest that the strain modulated SiNRs may have potential applications in the field effect nanodevice.