Let $(M,\omega,J,g)$ be a closed Kähler n-manifold, and $p\in M$. Assume that the sectional curvature $K_{g}$ satisfies

$$\sup_{M}K_{g}\leq 1,$$

and there is a smooth holomorphic m-submanifold $N$ such that $p\in N$, and

$$\int_{N}\omega^{m}<\frac{(m-1)!\pi}{2}\varpi_{m-1}.$$

Then the injectivity radius $i_{g}(p)$ of $(M,g)$ at $p$ satisfies that

$$i_{g}(p)^{m}\leq\frac{\pi^{m-1}}{(m-1)!2^{m-1}\varpi_{m-1}}\int_{N}\omega^{m}.$$