Brain development is fastest at the end of pregnancy and soon after birth. Neonatal brain function can thus offer fundamental insights into brain organization, but many existing functional neural measures are poor predictors of chronological age. Analysis of signal complexity (e.g. entropy) has been demonstrated to be powerful methodology in various fields of research, including life sciences. In this cross-validation study, our aim is to investigate functional brain entropy as a biomarker for neonatal brain age. We have performed supervised machine learning based regression with the Developing Human Connectome Project (dHCP) neonatal dataset (N=599), and predicted brain age in terms of both postmenstrual and postnatal age using the sample entropy of rs-fMRI-derived blood-oxygen-level-dependent (BOLD) signal from 90 regions across the neonatal brain as predictors. The BOLD signal is known to include confounding low-frequency oscillations, overlapping the frequency range of interest thought to represent neural activation, for which reason we performed finite impulse response filtering to a safe frequency range (0.04 – 0.07 Hz). The analysis was performed separately for both definitions of brain age as target variable, as well as for term-born participants only (N=483) and the full sample. Our results demonstrate moderate to relatively high prediction accuracy (test R²’s 0.11 – 0.37) for the different analysis settings on entropy measures, outperforming BOLD signal power as predictors (test R²’s 0.08 – 0.16). For interpretability, we have plotted the most important model coefficients. We conclude that the BOLD signal sample entropy can used as an effective biomarker for neonatal brain age.