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In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator Lp,γ,αu =▽γ · (|▽γu|p-2pα▽γu) on Rm+n with singularity at the origin,where ▽γ is the gradient operator defined by ▽γ =(▽x,|x|γ▽y) and p is the distance function.As an application,we get some Hardy type inequalities associated with ▽γ.