In this paper, using the direct and fixed point methods, we have established the generalized Hyers-Ulam stability of the following additivequadratic functional equation f(2x + y) + f(2x - y) = 2[f(x + y) + f(x - y)] + 2[f(x) + f(-x)] - [f(y) + f(-y)], in random normed spaces.