Suppose that \(X:=(X,\|\cdot\|)\) is a Banach space and \(\leq\) is a partial order on \(X\) such that the order intervals \(\{x\in X:a\leq x\}\) and \(\{x\in X:x\leq a\}\) are closed and convex for all \(a\in X\). In this paper, the authors prove a weak convergence theorem for a fixed point of a monotone nonexpansive mapping in a Banach space with Opial’s condition. Recall that \(T:C\to C\), where \(C\) is a bounded closed convex subset of \(X\), is a monotone nonexpansive mapping if \(Tx\leq Ty\) and \(\|Tx-Ty\|\leq\|x-y\|\) for all \(x,y\in C\) with \(x\leq y\).