•Anticoagulation in liver disease and atrial fibrillation may reduce thromboembolic risk.•Anticoagulation in liver disease and atrial fibrillation is not associated with increased bleeding.•Only a minority of patients with liver disease and atrial fibrillation receive anticoagulation. Balancing the risk of thromboembolism and bleeding in patients with liver disease and atrial fibrillation/flutter is particularly challenging. To examine the risks of thromboembolism and bleeding with use/non-use of oral anticoagulation (including vitamin K-antagonists and direct oral anticoagulants) in patients with liver disease and AF. Danish nationwide register-based cohort study of anticoagulant naive individuals with liver disease, incident atrial fibrillation/flutter, and a CHA2DS2-VASc-score≥1 (men) or ≥2 (women), alive 30 days after atrial fibrillation/flutter diagnosis. Thromboembolism was a composite of ischaemic stroke, transient ischaemic attack, or venous thromboembolism. Bleeding was a composite of gastrointestinal, intracerebral, or urogenital bleeding requiring hospitalisation, or epistaxis requiring emergency department visit or hospital admission. Cause-specific Cox-regression was used to estimate absolute risks and average risk ratios standardised to covariate distributions. Because of significant interactions with anticoagulants, results for thromboembolism were stratified for CHA2DS2-VASc-score, and results for bleeding were stratified for cirrhotic/non-cirrhotic liver disease. Four hundred and nine of 1,238 patients with liver disease and new atrial fibrillation/flutter initiated anticoagulants. Amongst patients with a CHA2DS2-VASc-score of 1–2 (2–3 for women), five-year thromboembolism incidence rates were low and similar in the anticoagulant (6.5%) versus no anticoagulant (5.5%) groups (average risk ratio 1.19 95%CI, 0.22–2.16). In patients with a CHA2DS2-VASc-score>2 (>3 for women), incidence rates were 16% versus 24% (average risk ratio 0.66 95%CI, 0.45–0.87). Bleeding risks appeared higher amongst patients with cirrhotic versus non-cirrhotic disease but were not significantly affected by anticoagulant status. Oral anticoagulant initiation in patients with liver disease, incident new atrial fibrillation/flutter, and a high CHA2DS2-VASc-score was associated with a reduced thromboembolism risk. Bleeding risk was not increased with anticoagulation, irrespective of the type of liver disease.