In this paper, we apply fixed point technique to investigate the following additive functional inequality: \[ \|f(x)+f(y)+f(z)+f(w)\|eq\|f(x+y)+f(z+w)\| \] in normed modules over a $C^*$-algebra, which is also applied to understand homomorphisms in $C^*$-algebras. Our results improve and generalize some results given by some authors. Especially, we get a better error estimation of An's main result.