Background: Children with X-linked hypophosphataemia have high concentrations of circulating phosphatonin fibroblast growth factor 23 (FGF23), which causes renal phosphate wasting and hypophosphataemia, rickets, skeletal deformities, and growth impairment. Burosumab, a human monoclonal antibody against FGF23, improves phosphate homoeostasis and rickets in children aged 5–12 years with X-linked hypophosphataemia. We aimed to assess the safety and efficacy of burosumab in younger children with X-linked hypophosphataemia. Methods: In this open-label, phase 2 trial at three hospitals in the USA, children (aged 1–4 years) with X-linked hypophosphataemia received burosumab (0·8 mg/kg) via subcutaneous injection every 2 weeks for 64 weeks. The dose was increased to 1·2 mg/kg if two consecutive pre-dose serum phosphorus concentrations were below 1·03 mmol/L (3·2 mg/dL), serum phosphorus had increased by less than 0·16 mmol/L (<0·5 mg/dL) from baseline, and a dose of burosumab had not been missed. Participants could continue to receive burosumab for up to an additional 96 weeks during the extension period. Key inclusion criteria were age 1–4 years at the time of informed consent; fasting serum phosphorus concentration of less than 0·97 mmol/L (3·0 mg/dL); serum creatinine 8·8–35·4 μmol/L (0·1–0·4 mg/dL); radiographic evidence of rickets (at least five participants were required to have a Thacher Rickets Severity Score of ≥1·5 at the knee); and a confirmed PHEX mutation or a variant of unknown significance in the patient or direct relative also affected with X-linked hypophosphataemia. Conventional therapy was stopped upon enrolment. The coprimary endpoints were safety and change from baseline to week 40 in fasting serum phosphorus concentrations. Changes in rickets severity from baseline to weeks 40 and 64 (assessed radiographically using Thacher Rickets Severity Score and an adaptation of the Radiographic Global Impression of Change), and recumbent length or standing height, were key secondary outcomes. This trial is registered with ClinicalTrials.gov, number NCT02750618, and is ongoing. Findings: Between May 16, 2016, and June 10, 2016, we enrolled 13 children with X-linked hypophosphataemia. All 13 children completed 64 weeks of treatment and were included in the efficacy and safety analysis; none exceeded 70 weeks of treatment at the time of analysis. Serum phosphorus least squares mean increase from baseline to week 40 of treatment was 0·31 mmol/L (SE 0·04; 95% CI 0·24–0·39; 0·96 mg/dL [SE 0·12]; p<0·0001). All patients had at least one adverse event. 14 treatment-related adverse events, mostly injection site reactions, occurred in five children. One serious adverse event considered unrelated to treatment (tooth abscess) occurred in a child with a history of tooth abscess. All other adverse events were mild to moderate, except a severe food allergy considered unrelated to treatment. No instances of nephrocalcinosis or noteworthy changes in the results of a standard safety chemistry panel emerged. Total Thacher Rickets Severity Score decreased by a least squares mean of −1·7 (SE 0·1; p<0·0001) from baseline to week 40 and by −2·0 (SE 0·1; p<0·0001) by week 64. The Radiographic Global Impression of Change score also indicated significant improvement, with a least squares mean score of +2·3 (SE 0·1) at week 40 and +2·2 (0·1) at week 64 (both p<0·0001). Mean length or standing height Z score was maintained from baseline to week 64. Interpretation: Burosumab had a favourable safety profile, increased serum phosphorus, and improved rickets and prevented early declines in growth in children aged 1–4 years with X-linked hypophosphataemia. These findings could substantially alter the treatment of young children with X-linked hypophosphataemia. Funding: Ultragenyx Pharmaceutical and Kyowa Kirin International.