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We find that an intrinsic curvature affects greatly the mechanical property of a semiflexible biopolymer.We model the semiflexible biopolymer as an elastic filament.It is well know that a filament with intrinsic torsion and curvature can form a helix.We show analytically that the extension of a helical filament with proper intrinsic torsion and curvature can undergo a one-step discontinuous transition.This agrees quantitatively with experimental observations for a helix in a chemically defined lipid concentrate.We find that with moderate intrinsic curvature and bending rigidity, the extension of a two-dimensional semiflexible biopolymer also exhibits a sharp first order transition at finite temperature.