Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation f ( x + 2 y ) + f ( x − 2 y ) = 4 f ( x + y ) + 4 f ( x − y ) − 6 f ( x ) + f ( 2 y ) + f ( − 2 y ) − 4 f ( y ) − 4 f ( − y ) in Banach spaces.