Summary: Consider a supercritical Crump-Mode-Jagers process \(( \mathcal{Z}_{t}^{\varphi})_{t \geq 0}\) counted with a random characteristic \(\varphi\). Nerman’s celebrated law of large numbers [O. Nerman, Z. Wahrscheinlichkeitstheor. Verw. Geb. 57, 365–395 (1981; Zbl 0451.60078)] states that, under some mild assumptions, \(e^{-\alpha t} \mathcal{Z}_{t}^{\varphi}\) converges almost surely as \(t \to \infty\) to \(aW\). Here, \(\alpha > 0\) is the Malthusian parameter, \(a\) is a constant and \(W\) is the limit of Nerman’s martingale, which is positive on the survival event. In this general situation, under additional (second moment) assumptions, we prove a central limit theorem for \((\mathcal{Z}_{t}^{\varphi})_{t \geq 0}\). More precisely, we show that there exist a constant \(k \in \mathbb{N}_{0}\) and a function \(H(t)\), a finite random linear combination of functions of the form \(t^{j} e^{\lambda t}\) with \(\alpha/2 \leq \mathrm{Re}(\lambda) < \alpha\), such that \(( \mathcal{Z}_{t}^{\varphi} - ae^{\alpha t} W - H(t)) / \sqrt{t^{k} e^{\alpha t}}\) converges in distribution to a normal random variable with random variance. This result unifies and extends various central limit theorem-type results for specific branching processes.