The band gap engineering of nano-structure is the key point in application of nano electronic device. By using first-principles calculations, the band structures of graphyne nanoribbons with armchair (a-GNRs) and zigzag (z-GNRs) edges under various strains are investigated. A controllable band gap of strained narrow a-GNR (1.36~2.85 eV) could be modulated almost linearly under an increasing strain in range of -5% ~ 16%. In contrast, the band gap of strained narrow z-GNR (2.68 ~ 2.91 eV)is relatively insensitive to -16% ~ 16% strain. This contrastive band gap engineering of narrow GNRs is attributed to different structure deformation of the specific graphyne structure including two kinds of carbon atoms different from graphene. For wider strained GNRs, the band gap depending on its width and edge morphology generally decreases as tensile strain increases, similar to 2D graphyne sheet. The charge density distributions of key states around Fermi level are presented