The aim of the article is to establish an analog of the Lagrange mean value theorem for the case of vector-valued mappings. The main result of the article reads as follows: Let \(f\:[\alpha,\beta]\to\mathbb R^m\) be a continuous function on \([\alpha,\beta]\subset \mathbb R\) and differentiable on the interval \((\alpha,\beta)\), where \(m\geq 1\) and \(\alpha < \beta\); then \(\bigl(f(\alpha) - f(\beta)\bigr)/(\beta - \alpha)\) is a convex combination of \(m\) values of \(f'\), i.e., there exist numbers \(\xi_i\in (\alpha,\beta)\) and \(p_i\), \(i = 1,\dots,m\), such that \[ \frac{f(\beta) - f(\alpha)}{\beta - \alpha} = \sum_{i=1}^m p_if'(\xi_i),\quad p_i\geq 0,\;\sum_{i=1}^m p_i = 1. . \]