We investigate the following weighted elliptic equation −∆u + b(x) · ∇u = (1 + |x| 2) α 2 u p in R N, where α ≥ 0, p > 1, N ≥ 3 and the advection term b(x) is a smooth vector field satisfying certain decay condition. We establish a Liouville-type theorem for possible stable solutions of the equation above.