For a Kac-Moody algebra $\mathfrak{g}$ of rank $2$ and a fundamental weight $λ$, we explicitly give an isomorphism between the set of Lakshmibai-Seshadri paths $\mathbb{B}(λ)$ and monomial realization $\mathcal{M}(λ)$. As an application, we also give an explicit form of monomial realization $\mathcal{M}(λ)$ in terms of Weyl groups.