Objective: The aim of this study is the investigation of early-life EEG background abnormalities or “dysmature” traits in infants with tuberous sclerosis complex (TSC) and their capacity to predict autism spectrum disorder or neurodevelopmental outcome. Methods: EEG data were prospectively collected from TSC patients during the EPISTOP trial (NCT02098759). Subjects were younger than 4 months, and ASD risk and neurodevelopmental outcome were assessed at the age of 2 years. The EEG at the first visit was analyzed by means of Multiscale Entropy (MSE), multifractality (MFA), amplitude integrated EEG features and topological indices of the EEG network. These features were associated with both ASD and abnormal Bayley outcome of the infants using linear discriminant analysis. Results: The classification of the ASD patients shows that MFA and MSE had the best discrimination performances, with an area under the ROC curve AUC (MFA) = 0.74 and AUC(MSE) = 0.79 respectively, and kappa scores of Kappa(MFA) = 0.48 and Kappa(MSE) = 0.26. Concerning both abnormal Bayley outcome and ASD, the developmental abnormalities detection shows that entropy and fractal features outperform the other subsets of attributes and the multiclass analysis shows that those features can also discriminate patients with ASD from patients with only developmental abnormalities (Kappa(MFA) = 0.41 and Kappa(MSE) = 0.36). Conclusion: Quantitative EEG analysis shows that a dysmature EEG, i.e. a signal with higher fractal regularity and lower entropy, is associated with autism spectrum disorder or abnormal Bayley outcome at 2 years of age.