In this paper, the multiplicity of $-1$ as an eigenvalue of the adjacency matrix of a tree $T$ is studied and denoted by $m(T, -1)$. It is proven that among all trees $T$ with ${p\geq 2}$ pendant vertices, the maximum value of $m(T, -1)$ is $p-1$. Moreover, it is proven that for a tree with $p \geq 2$ pendant vertices, $m(T, -1) =p-1$ if and only if $T$ is a path with $n$ vertices with $n \equiv 2 \pmod 3$, or $T$ is a tree in which $d(v,u) \equiv 2 \pmod 3$, for any pendant vertex $v$ and any vertex $u$ of $T$ of degree at least 3, where $d(v,u)$ represents the distance between $v$ and $u$. Additionally, a lower bound for $m(T, -1)$ in terms of the number of pendant vertices is given.