  In this paper, we calculate the dimension of root spaces
$\mathfrak{g}_{\lambda}$ of a special type rank $3$ Kac-Moody algebras
$\mathfrak{g}$. We first introduce a special type of elements in
$\mathfrak{g}$, which we call elements in standard form. Then, we prove that
any root space is spanned by these elements. By calculating the number of
linearly independent elements in standard form, we obtain a formula for the
dimension of root spaces $\mathfrak{g}_{\lambda}$, which depends on the root
$\lambda$.
