Summary: Let \(\mathbb{D}\) be the unit disk in \(\mathbb{C}\), \(\mathbb{B}^k\) be the Euclidean unit ball in \(\mathbb{C}^k\), \(\Omega\) is a domain in \(\mathbb{C}^k\) (or \(\mathbb{C}\)). Let \(H_n(\mathbb{D},\Omega)\) be the set of all holomorphic mappings \(f\) from \(\mathbb{D}\) into \(\Omega\) which satisfies a certain condition. In this paper, it is proved that if \(f\in H_n(\mathbb{D},\mathbb{D})\), then \[ |f'(z)|\leq\frac{n|z|^{n-1}}{1-|z|^{2n}}(1-|f(z)|^2),\;z\in \mathbb{D}. \] Meanwhile, we obtain a similar result for the modulus of mappings in \(H_n(\mathbb{D},\mathbb{B}^k)\). The result generalizes the corresponding result in a literature.