  Let $\mathfrak P$ be the Lie algebra of Hamiltonian vector fields on the
torus, which is also known as the Virasoro-like algebra, a special kind of the
so-called Block type Lie algebra. And let $\mathfrak A$ be the Laurent
polynomial algebra in two variables. In this paper, by following S.E. Rao's
strategy of "backward induction", we prove that any quasi-finite simple
$(\mathfrak A,\mathfrak P)$-module has to come from Larsson-Shen's
construction.
