The synergistic regulation mechanism of uniaxial strain, topological defects, edge passivation atom and nanoribbon width on the geometric and electronic structures of zigzag graphene nanoribbons have been studied systematically by first-principles. It is found that the average formation energy and strain energy of X-N1N2-LD-ZGNR (X=H, F and O, as well as, N1=N2=3, 4 and 5) increase with the increase of uniaxial strain, and this relationship is also dependent of edge passivation atom species and nanoribbon width. And the edge of 55-LD-ZGNR passivating with O and F atoms is more beneficial than H atom for system stability. The stress-strain curve shows that the limiting strain of zigzag graphene nanoribbon depends on edge passivation atom species and nanoribbon width. The Young's modulus in the case of ε>3% and Poisson's ratio except O-33-LD-ZGNR at ε=1% of X-N1N2-LD-ZGNR decrease with the increase of the tensile strain, and is dependent of nanoribbon width and edge atom species. And O-55-LD-ZGNR is easier than F-55-LD-ZGNR and H-55-LD-ZGNR to be stretched or compressed. The magnetism is induced in both H-55-LD-ZGNR and F-55-LD-ZGNR, and remains with the increases of uniaxial tension strain. What is more, magnetic property of O-55-LD-ZGNR can be regulated by applying uniaxial strain, and the band gap of the O-N1N2-LD-ZGNR (N1=N2=3, 4 and 5) system can be regulated by adjusting the uniaxial tensile strain and nanoribbon width. Our research provides a new method to open the graphene band gap, which can provide some new theoretical guidance for the application of graphene in electronic devices and other fields. The band gap of the O-LD-ZGNDR system is opened as the uniaxial tensile strain increases.