We find that the excluded volume interaction (EVI) can accelerate an abrupt transition in extension for an intrinsically curved two-dimensional semiflexible biopolymer. It makes the transition much sharper, reduces the critical force remarkably, and the larger the persistent length or the intrinsic curvature, the larger the reduction in critical force. The transition is caused by a collective change in bending angles associated with removing cusps owing to thermal fluctuation. Our results reveal that EVI can excite a cooperative behavior, straighten more bonds simultaneously so cause a sharper transition. The transition is dominated by the mechanical force because the specific heat does not divergence. Our findings suggest that an intrinsically curved biopolymer can act as a switch or sensor in some biological processes.