Background: After acute coronary syndrome, diabetes conveys an excess risk of ischaemic cardiovascular events. A reduction in mean LDL cholesterol to 1·4–1·8 mmol/L with ezetimibe or statins reduces cardiovascular events in patients with an acute coronary syndrome and diabetes. However, the efficacy and safety of further reduction in LDL cholesterol with an inhibitor of proprotein convertase subtilisin/kexin type 9 (PCSK9) after acute coronary syndrome is unknown. We aimed to explore this issue in a prespecified analysis of the ODYSSEY OUTCOMES trial of the PCSK9 inhibitor alirocumab, assessing its effects on cardiovascular outcomes by baseline glycaemic status, while also assessing its effects on glycaemic measures including risk of new-onset diabetes. Methods: ODYSSEY OUTCOMES was a randomised, double-blind, placebo-controlled trial, done at 1315 sites in 57 countries, that compared alirocumab with placebo in patients who had been admitted to hospital with an acute coronary syndrome (myocardial infarction or unstable angina) 1–12 months before randomisation and who had raised concentrations of atherogenic lipoproteins despite use of high-intensity statins. Patients were randomly assigned (1:1) to receive alirocumab or placebo every 2 weeks; randomisation was stratified by country and was done centrally with an interactive voice-response or web-response system. Alirocumab was titrated to target LDL cholesterol concentrations of 0·65–1·30 mmol/L. In this prespecified analysis, we investigated the effect of alirocumab on cardiovascular events by glycaemic status at baseline (diabetes, prediabetes, or normoglycaemia)—defined on the basis of patient history, review of medical records, or baseline HbA_1c or fasting serum glucose—and risk of new-onset diabetes among those without diabetes at baseline. The primary endpoint was a composite of death from coronary heart disease, non-fatal myocardial infarction, fatal or non-fatal ischaemic stroke, or unstable angina requiring hospital admission. ODYSSEY OUTCOMES is registered with ClinicalTrials.gov, number NCT01663402. Findings: At study baseline, 5444 patients (28·8%) had diabetes, 8246 (43·6%) had prediabetes, and 5234 (27·7%) had normoglycaemia. There were no significant differences across glycaemic categories in median LDL cholesterol at baseline (2·20–2·28 mmol/L), after 4 months' treatment with alirocumab (0·80 mmol/L), or after 4 months' treatment with placebo (2·25–2·28 mmol/L). In the placebo group, the incidence of the primary endpoint over a median of 2·8 years was greater in patients with diabetes (16·4%) than in those with prediabetes (9·2%) or normoglycaemia (8·5%); hazard ratio (HR) for diabetes versus normoglycaemia 2·09 (95% CI 1·78–2·46, p<0·0001) and for diabetes versus prediabetes 1·90 (1·65–2·17, p<0·0001). Alirocumab resulted in similar relative reductions in the incidence of the primary endpoint in each glycaemic category, but a greater absolute reduction in the incidence of the primary endpoint in patients with diabetes (2·3%, 95% CI 0·4 to 4·2) than in those with prediabetes (1·2%, 0·0 to 2·4) or normoglycaemia (1·2%, −0·3 to 2·7; absolute risk reduction p_interaction=0·0019). Among patients without diabetes at baseline, 676 (10·1%) developed diabetes in the placebo group, compared with 648 (9·6%) in the alirocumab group; alirocumab did not increase the risk of new-onset diabetes (HR 1·00, 95% CI 0·89–1·11). HRs were 0·97 (95% CI 0·87–1·09) for patients with prediabetes and 1·30 (95% CI 0·93–1·81) for those with normoglycaemia (p_interaction=0·11). Interpretation: After a recent acute coronary syndrome, alirocumab treatment targeting an LDL cholesterol concentration of 0·65–1·30 mmol/L produced about twice the absolute reduction in cardiovascular events among patients with diabetes as in those without diabetes. Alirocumab treatment did not increase the risk of new-onset diabetes. Funding: Sanofi and Regeneron Pharmaceuticals.