Based on first-principles method we predict a new low-energy Stone-Wales graphene SW40, which has an orthorhombic lattice with Pbam symmetry and 40 carbon atoms in its crystalline cell forming well-arranged Stone-Wales patterns. The calculated total energy of SW40 is just about 133 meV higher than that of graphene, indicating its excellent stability exceeds all the previously proposed graphene allotropes. We find that SW40 processes intrinsic Type-III Dirac-cone (Phys. Rev. Lett., 120, 237403, 2018) formed by band-crossing of a local linear-band and a local flat-band, which can result in highly anisotropic Fermions in the system. Interestingly, such intrinsic type-III Dirac-cone can be effectively tuned by inner-layer strains and it will be transferred into Type-II and Type-I Dirac-cones under tensile and compressed strains, respectively. Finally, a general tightbinding model was constructed to understand the electronic properties nearby the Fermi-level in SW40. The results show that type-III Dirac-cone feature can be well understood by the π-electron interactions between adjacent Stone-Wales defects. PACS numbers:The experimental synthesizing of two-dimensional (2D) graphene 1-3 and graphdiynes 4,5 opened the door to the 2D carbon-word and have attracted much scientific efforts to reveal their fundamental properties and potential applications 1,6-9 . With excellent mechanical and electronic properties 1,6,7 , graphene is believed as a potential candidate for replacing silicon in future nano-electronics as new building block 10 . To design pure-carbon nano-divice, 2D carbon allotropes can provide us rich electronic properties for different functional requirements. For example, R 57−1 11 , R 57−2 12 , H 567 12 , O 567 12 , ψ-graphene 13,14 , OPG-L 33 , net-τ 15 and other 2D carbon allotropes 16-24 with normal metallic property can be used as electron conductors. The semiconducting octite SC 19 , pza-C10 25 , Θ-graphene 26,27 and γ-graphyne 28,29 are proper candidates 23,30,31 for building diodes and transistors. The graphene 1-3 , phagraphene 32 , OPG-Z 33 and SWgraphene 23 as Dirac-cone semi-metals 23,30,31 with high carrier mobility can be used to construct high-speed nano-device. Especially, the freedom of rotation in graphene bilayer bring us the surprising phenomenon of superconductivity in some magic degrees [34][35][36][37] , which has set off a new round of research upsurge on low-dimensional carbon systems [38][39][40][41] .