It is known that, for a maximal collection $\mathcal{A}$ of pairwise disjoint non-parallel essential annuli in a handlebody of genus 2, $1 \leq |\mathcal{A}| \leq 3$. We show that for a maximal collection $\mathcal{A}$ of pairwise disjoint non-parallel essential annuli in a handlebody of genus n (≥ 3), $|\mathcal{A}|\leq 4n - 5$, and the bound is best possible.