In this paper, we consider the following quasilinear elliptic equation with Hardy potential and Dirichlet boundary condition: -Sigma(N)(i,j=1) D-j(a(i j)(x, u)D(i)u) + 1/2 Sigma(N)(i,j=1) D(s)a(i,j)(x, u)D(i)uD(j)u - lambda|x|(-2)u = f (x, u) in Omega, where Omega subset of R-N (N >= 3) is a smooth bounded domain, D-i = partial derivative/partial derivative x(i), D(s)a(i j)(x, s) = partial derivative/partial derivative s a(i j)(x, s), and 0