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In this paper, we complete the classification of the {\bf Z}-graded modulesof the intermediate series over the $q$-analog Virasoro-like algebra $L$. Wefirst construct four classes of irreducible {\bf Z}-graded $L$-modules of theintermediate series. Then we prove that any {\bf Z}-graded $L$-modules of theintermediate series must be the direct sum of some trivial $L$-modules or oneof the modules constructed by us.

The classification of $\bf Z$-graded modules of the intermediate series over the $q$-analog Virasoro-like algebra