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We consider the anisotropic quasilinear elliptic Dirichlet problem $$\left\{\begin{array}{cc}{\displaystyle -\sum _{i=1}^N{D}^i{a}_i(x,u,\nabla u)+{\left|u\right|}^{s\left(x\right)-1}u=f+\lambda \frac{{\left|u\right|}^{p_0\left(x\right)-2}u}{{\left|x\right|}^{p_0\left(x\right)}}}\hfill & \text{in}\Omega ,\hfill \\ u=0\hfill & \text{on}\partial \Omega ,\hfill \end{array}\right.$$ where $\Omega$ is an open bounded subset of ${ℝ}^N$ containing the origin. We show the existence of entropy solution for this equation where the data $f$ is assumed to be in $L^1\left(\Omega \right)$ and $\lambda$ is a positive constant.