We investigate the transport properties of defected graphene nanoribbons with single C vacancy using non-equilibrium Green's function formalism within the tight-binding model approach. The insights derived from the analysis of geometric and electronic structure allow us to infer the localized nature of the defect-induced structure relaxation and transport properties. We show that the single vacancy position and concentration in graphene nanoribbons can alter the transmission spectrum and current-voltage characteristics. We consider the dependence of the transport properties on the local strain caused by the C vacancy positions and concentration. We conclude that such defect profoundly modifies the mechanical and electronic properties of the graphene nanoribbons, and introduce new transport properties by allowing the atomic rearrangement.