In this paper we solve a generalized quadratic Jensen type functional equation $m^2 f (frac{x+y+z}{m}) + f(x) + f(y) + f(z) =n^2 [f(frac{x+y}{n}) +f(frac{y+z}{n}) +f(frac{z+x}{n})]$ and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.