Background The role of sleep in cognitive processes has been confirmed by a growing number of reports for all ages of life. Analysing sleep electroencephalogram (EEG) spectra may be useful to study cortical organisation in individuals with Borderline Intellectual Functioning (BIF), as seen in other disturbances even if it is not considered a disease. The aim of this study was to determine if the sleep EEG power spectra in children with BIF could be different from typically developing children. Methods Eighteen BIF (12 males) (mean age 11.04; SD ± 1.07) and 24 typical developing children (14 men) (mean age 10.98; SD ± 1.76; P = 0.899) underwent an overnight polysomnography (PSG) recording in the Sleep Laboratory of the Clinic of Child and Adolescent Neuropsychiatry, after one adaptation night. Sleep was subdivided into 30‐s epochs and sleep stages were scored according to the standard criteria and the power spectra were calculated for the Cz‐A2 channel using the sleep analysis software Hypnolab 1.2 (SWS Soft, Italy) by means of the Fast Fourier Transform and the power spectrum was calculated for frequencies between 0.5 and 60 Hz with a frequency step of 1 Hz and then averaged across the following bands delta (0.5–4 Hz), theta (5–7 Hz), alpha (8–11 Hz), sigma (11–15 Hz), and beta (16–30 Hz), gamma (30–60 Hz) for S2, SWS and REM (Rapid Eye Movement) sleep stages. Results BIF have a reduced sleep duration (total sleep time; P < 0.001), and an increased rate of stage shifts (P < 0.001) and awakenings (P < 0.001) and WASO (wakefulness after sleep onset) % (P < 0.001); the stage 2% (P < 0.001), and REM% (P < 0.001) were lower and slow‐wave sleep percentage was slightly higher (P < 0.001). All children with BIF had an AHI (apnoea–hypopnea index) less than 1 (mean AHI = 0.691 ± 0.236) with a mean oxygen saturation of 97.6% and a periodic leg movement index (PLMI) less than 5 (mean PLMI = 2.94 ± 1.56). All sleep stages had a significant reduction in gamma frequency (30–60 Hz) (P < 0.001) and an increased delta frequency (0.5–4.0 Hz) (P < 0.001) power in BIF subjects compared with typically developing children. Conclusion Our findings shed light on the importance of sleep for cognition processes particularly in cognitive borderline dysfunction and the role of EEG spectral power analysis to recognize sleep characteristics in BIF children.