Abstract: Let $ \mathcal{A} $ be an algebra with unit 1. A map $ f:\mathcal{A}\rightarrow \mathcal{A} $ is a weakly additive map if for every $ x,y\in\mathcal{A} $ there exist $ t_{x,y},s_{x,y}\in \mathbb{F} $ such that $ f(x+y) = t_{x,y}f(x)+s_{x,y}f(y) $. We prove that under some conditions, if $ f $ is a commuting map, then there exists $ \lambda_{0}(x)\in \mathcal{A} $ and a map $ \lambda_{1} $ from $ \mathcal{A} $ into $ Z(\mathcal{A}) $ such that $ f(x) = \lambda_{0}(x) x+\lambda_{1}(x) $ for all $ x\in \mathcal{A} $. As an application, a class of commuting weakly additive maps on $ M_{n}(\mathbb{F}) $ are characterized.