We apply Monte Carlo simulation method to lattice systems to study the effect of an intrinsic curvature on the mechanical property of a semiflexible biopolymer. We find that when the intrinsic curvature is sufficient large, the extension of a semiflexible biopolymer can undergo a first-order transition at finite temperature. The critical force increases with increasing intrinsic curvature. But the relationship between the critical force and the bending rigidity is structure-dependent. In triangle lattice system, when the intrinsic curvature is smaller than a critical value, the critical force increases with the increasing bending rigidity first, and then decreases with the increasing bending rigidity. But in square lattice system, the critical force always decreases with the increasing bending rigidity. In contrast, when the intrinsic curvature is greater than the critical value, the larger bending rigidity always results in a larger critical force in both lattice systems.