The physical properties of transition metal dichalcogenides (TMDs) with a few layers can be tailored by strain engineering because of the good elasticity with a strain limit of more than 10 %. In this work, elastic deformation under uniaxial tension in single-layer MoS2 nano-sheets is investigated theoretically by molecular dynamics simulation. A size-dependent elastic modulus is observed especially from sheets with a width of less than 10 nm. The elastic modulus of the nano-sheets with zigzag edges decreases as the width becomes narrower but that of the nano-sheets with armchair edges increases anomalously. The anisotropic behavior is ascribed to the opposite variation of the edge stress induced by the atomic configurations at the edges. Based on the continuum theory, a composite model composed of edge and core regions is established and the parameter, alpha, is adopted to describe the edge stiffness. The value of alpha is negative and positive for the zigzag and armchair edges, respectively, but the fitted edge width is 0.63 nm that is independent of the edge chirality.