In this paper we study general solutions and generalized Hyers-Ulam-Rassias stability of the following function equation $$f(x-sum^{k}_{i=1}x_i)+(k-1)f(x)+(k-1)sum^{k}_{i=1}(x_i)=f(x-x_1)+sum^{k}_{i=2}f(x_i-x)+sum^{k}_{i=1}sum^{k}_{j=1,j > i}f(x_i+x_j)$$. for $k{geq}2$, on non-Archimedean Banach spaces. It will be proved that this equation is equivalent to the so-called quadratic functional equation.