Previous　rolling　soft　robots　are　usually　hard　to　achieve　balanced　rolling　performance　(terrain　adaptability,　rolling　velocity　and　energy　efficiency).　This　paper　proposes　a　rolling　soft　robot　driven　by　local　curvature　loading,　which　demonstrates　good　rolling　velocity,　small　deformation　rate,　good　energy　efficiency　and　excellent　terrain　adaptability.　A　theory　based　on　the　energy　method　is　established　to　analyze　the　rolling　mechanism　of　the　soft　robot　and　to　determine　the　critical　loading　curvature,　which　is　validated　by　experiments.　The　local　curvature　loading　causes　the　deformation　of　the　entire　robot　configuration　and　results　in　the　shift　of　the　gravity　center,　which　generates　a　gravity　torque　to　drive　the　rolling　of　the　soft　robot　when　the　critical　loading　curvature　is　reached.　The　proposed　soft　robot　has　good　average　rolling　velocity　(182.9　mm/s　or　0.938　body　length　per　second,　BL/s)　and　can　adapt　to　a　variety　of　complex　terrains　such　as　the　stairs　(stair　height　15　mm),　the　slope　(slope　angle　12.4　°)　and　the　wide　broken　bridge　(gap　length　100　mm　or　0.526　BL).　The　study　in　this　work　demonstrates　broad　application　prospect　in　the　fields　of　biomedical　therapy,　exploration,　searching　and　rescuing,　which　provides　a　new　idea　for　the　structural　design　and　performance　improvement　of　rolling　soft　robots.　©　2025　Elsevier　B.V.