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}).
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