Let $\mathcal{T}$ be a Galton-Watson tree with a given offspring distribution $ξ$, where $ξ$ is a $Z_{\geq 0}$-valued random variable with $E[ξ] = 1$ and $0 < σ^{2}:=Var[ξ] < \infty$. For $n \geq 1$, let $T_{n}$ be the tree $\mathcal{T}$ conditioned to have $n$ vertices. In this paper we investigate $b(T_n)$, the burning number of $T_n$. Our main result shows that asymptotically almost surely $b(T_n)$ is of the order of $n^{1/3}$.