Metal-organic frameworks (MOFs) have attracted a great deal of interest from both academia and industry due to their extensive potential applications. The tunable physical properties through the manipulation of composition have led to increasing attention to the exploration of the MOF applications. However, the tunability of physical property of MOF with external mechanical load, which usually steams from actual fabrication and application processes, has been rarely investigated. Here, ab initio (first-principles) density functional theory (DFT) calculations are performed to investigate the mechanical, electrical properties and strain engineering of a typical metal-organic framework, MOF-5. Preliminary calculations by using different pseudopotentials and cut-off energies are performed to verify the adopted critical parameters in subsequent simulations. Both the structural stability of MOF-5 and the effect of applied strain are investigated from an energetic point of view. With the increase of applied strain, the cohesive energy of MOF-5 decreases, inducing the reduction of structural stability. In addition, the variation of cohesive energy of MOF-5 shows an asymmetry under expansive and compressive conditions. By applying strain along different directions, the mechanical properties of MOF-5 are systematically investigated, and mechanical constants including Young's modulus, Poisson ratio and elastic constants are obtained. In addition, by analyzing the band gap of MOF-5, the intrinsic electrical property of MOF-5 is clarified. The band gap of MOF-5 is 3.49 eV, indicating that MOF-5 is a wide bandgap semiconductor, which is represented by the combination effect of both [Zn4O]6+ metal clusters and organic linkers. Analysis on the strain engineering of electrical properties of MOF-5 reveals that the applied strain induces the decrease of band gap of MOF-5, and thus leading to the increase of conductivity. This transition is induced by the decrease of conduction energy-level. Further studies on the variations of PDOS and covalent bond show that the strain engineering of electrical property of MOF-5 intrinsically originates from the variation of covalent bond in the organic linker. The applied strain apparently weakens the covalent bond, and thus inducing the relaxation and redistribution of electrons, which increases the activities of electrons, and finally leads to the overall increase of conductivity of MOF-5. This theoretical study quantitatively clarifies the tunability of electronic band gap of MOF-5 with external strain, and provides a theoretical guidance in the design optimization and property evaluation of gas sensors based on MOF-5.