Let $(M,\omega,J,g,\Omega)$ be a closed Ricci-flat Calabi-Yau n-manifold, 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 special lagrangian submanifold $L$ of phase $\theta$ such that $p\in L$, and

$$\int_{L}{\rm Re}e^{\sqrt{-1}\theta}\Omega<\frac{\pi}{2n}\varpi_{n-1},$$

where $\varpi_{n-1}$ denotes 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

$$i_{g}(p)^{n}\leq\frac{n\pi^{n-1}}{2^{n-1}\varpi_{n-1}}\int_{L}{\rm Re}e^{\sqrt{-1}\theta}\Omega.$$