  In this paper, we studied the jet modules for the centerless Virasoro-like
algebra which is the Lie algebra of the Lie group of the area-preserving
diffeomorphisms of a $2$-torus. The jet modules are certain natural modules
over the Lie algebra of semi-direct product of the centerless Virasoro-like
algebra and the Laurent polynomial algebra in two variables. We reduce the
irreducible jet modules to the finite-dimensional irreducible modules over some
infinite-dimensional Lie algebra and then characterize the irreducible jet
modules with irreducible finite dimensional modules over $\mathfrak{sl}_2$. To
determine the indecomposable jet modules, we use the technique of polynomial
modules in the sense of \cite{BB, BZ}. Consequently, indecomposable jet modules
are described using modules over the algebra $\BB_+$, which is the "positive
part" of a Block type algebra studied first by \cite{DZ} and recently by
\cite{IM, I}).
