Let d be a positive integer, q=(qij)d×d be a d×d matrix, ℂq be the quantum torus algebra associated with q. We have the semidirect product Lie algebra
$\mathfrak{g}$=Der(ℂq)⋉Z(ℂq), where Z(ℂq) is the centre of the rational quantum torus algebra ℂq. In this paper, we construct a class of irreducible weight
$\mathfrak{g}$-modules
$\mathcal{V}$α (V,W) with three parameters: a vector α∈ℂd, an irreducible
$\mathfrak{gl}$d-module V and a graded-irreducible
$\mathfrak{gl}$N-module W. Then, we show that an irreducible Harish Chandra (uniformaly bounded)
$\mathfrak{g}$-module M is isomorphic to
$\mathcal{V}$α(V,W) for suitable α, V, W, if the action of Z(ℂq) on M is associative (respectively nonzero).