In this paper, we solve the QUADRATIC -functional equations 2f(x) + 2f(y) = f(x + y) + 2f( (x y)); (0. 1) where is a xed non-Archimedean number with 2 6= 3. Using the xed point method and the direct method, we prove the Hyers-Ulam stability of the functional equation (0. 1) in non-Archimedean Banach spaces.