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Consider a class of elliptic equation of the form $$-\Delta u-\frac{\lambda }{{\left|x\right|}^2}u=u^{2^{*}-1}+\mu u^{-q}\text{in}\Omega \setminus \left\{0\right\}$$ with homogeneous Dirichlet boundary conditions, where $0\in \Omega \subset {ℝ}^N$($N\ge 3$), $0<q<1$, $0<\lambda <{(N-2)}^2/4$ and $2^{*}=2N/(N-2)$. We use variational methods to prove that for suitable $\mu$, the problem has at least two positive weak solutions.