Let $(M,g)$ be a closed Riemannian manifold, $\Theta$ be a calibration n-form, and $p\in M$. Assume that the sectional curvature $K_{g}$ satisfies

$$\sup_{B_{g}(p,2\pi)}K_{g}\leq 1,$$

and there is a submanifold $L$ calibrated by $\Theta$ such that $\dim_{\mathbb{R}}L=n$, $p\in L$, and

$$\int_{L}\Theta<\frac{\pi}{2n}\varpi_{n-1},$$

where $\varpi_{n-1}$ is the volume of $S^{n-1}$ with the standard metric of constant curvature 1. Then the injectivity radius $i_{g}(p)$ of $(M,g)$ at $p$ satisfies that

$$i_{g}(p)^{n}\leq\frac{n\pi^{n-1}}{2^{n-1}\varpi_{n-1}}\int_{L}\Theta.$$