Introduction Over 18 000 children are admitted annually to UK paediatric intensive care units (PICUs), of whom nearly 75% receive respiratory support (invasive and/or non-invasive). Continuous positive airway pressure (CPAP) has traditionally been used to provide first-line non-invasive respiratory support (NRS) in PICUs; however, high-flow nasal cannula therapy (HFNC), a novel mode of NRS, has recently gained popularity despite the lack of high-quality trial evidence to support its effectiveness. This feasibility study aims to inform the design and conduct of a future definitive randomised clinical trial (RCT) comparing the two modes of respiratory support. Methods and analysis We will conduct a three-centre randomised feasibility study over 12 months. Patients admitted to participating PICUs who satisfy eligibility criteria will be recruited to either group A (primary respiratory failure) or group B (postextubation). Consent will be obtained from parents/guardians prior to randomisation in 'planned' group B, and deferred in emergency situations (group A and 'rescue' group B). Participants will be randomised (1:1) to either CPAP or HFNC using sealed, opaque envelopes, from a computer-generated randomisation sequence with variable block sizes. The study protocol specifies algorithms for the initiation, maintenance and weaning of HFNC and CPAP. The primary outcomes are related to feasibility, including the number of eligible patients in each group, feasibility of randomising >50% of eligible patients and measures of adherence to the treatment protocols. Data will also be collected on patient outcomes (eg, mortality and length of PICU stay) to inform the selection of an appropriate outcome measure in a future RCT. We aim to recruit 120 patients to the study. Ethics and dissemination Ethical approval was granted by the National Research Ethics Service Committee North East-Tyne&Wear South (15/NE/0296). Study findings will be disseminated through peer-reviewed journals, national and international conferences. Trials registration number NCT02612415; pre-results.