Respiration is governed by a widespread network of cortical and subcortical structures. This complex communication between the brain and lungs is altered in pathological conditions. Apnoea - the cessation of respiration - is a common condition in infants, particularly those born prematurely. Apnoea in infants is believed to relate to immaturity of brainstem respiratory centres; involvement of the cortex in respiration in infants has yet to be explored. We investigated if cortical control of respiration occurs in newborn humans and whether it relates to apnoea. Using simultaneous electroencephalography (EEG) and impedance pneumography, we show that cortico-respiratory coupling is present in premature and term newborns (104 recordings from 68 infants; 34.5 {+/-} 2.6 weeks post-menstrual age), identifying an interplay between breathing phase and EEG amplitude. We further shed light on the biological meaning by revealing that the strongest coupling occurs during inspiration and that cortical activity precedes respiration, with coupling strongest over frontocentral regions. These findings support the notion that the cortico-respiratory coupling observed here primarily constitutes communication between cortical motor areas and lung effectors. Moreover, we show that cortico-respiratory coupling is negatively correlated with the rate of apnoea, revealing novel mechanistic insight into this common and potentially life-threatening neonatal pathology.