  Let $G$ be a multiplicatively written finite group. We denote by $\mathsf
E(G)$ the smallest integer $t$ such that every sequence of $t$ elements in $G$
contains a product-one subsequence of length $|G|$. In 1961, Erd\H{o}s,
Ginzburg and Ziv proved that $\mathsf E(G)\leq 2|G|-1$ for every finite
solvable group $G$ and this result is well known as the Erd\H{o}s-Ginzburg-Ziv
Theorem. In 2010, Gao and Li improved this result to $\mathsf
E(G)\leq\frac{7|G|}{4}-1$ and they conjectured that $\mathsf E(G)\leq
\frac{3|G|}{2}$ holds for any finite non-cyclic group. In this paper, we
confirm the conjecture for all finite non-cyclic groups of odd order.
