Objective: It remains unclear whether people with HIV (PWH) have increased risk of aneurysms. We aimed to investigate if the risk of subarachnoid haemorrhage, cerebral aneurysm, aortic aneurysm and other arterial aneurysms and dissections is increased in PWH compared with the general population. Design: We performed a nationwide population-based matched cohort study. Methods: We compared PWH with age-matched and sex-matched comparison cohort members to calculate incidence rate ratios (IRR) of subarachnoid haemorrhage, cerebral aneurysm, aortic aneurysm and other arterial aneurysms and dissections as well as surgery for these conditions. Results: We included all PWH, who were Danish residents and treated at a HIV healthcare centre between January 1995 and February 2018 (n = 6935) and an age-matched and sex-matched comparison cohort (n = 55 480). PWH had increased risk of subarachnoid haemorrhage (IRR 1.7, 95% CI, 1.1-2.6), but no increased risk of surgery for this condition. PWH had no increased risk of cerebral aneurysm or aortic aneurysm or surgery for these conditions. The risk of other arterial aneurysms and dissections was increased in PWH (IRR 2.0, 95% CI, 1.4-2.9), but this only applied for PWH who reported intravenous substance use as a route of HIV transmission (IRR 18.4, 95% CI, 9.3-36.6), and not for PWH without reported injection drug use (IRR 1.2, 95% CI, 0.73-1.7). Conclusion: PWH were not at an increased risk of cerebral, aortic or other arterial aneurysms and dissections. Although PWH were at an increased risk of subarachnoid haemorrhage, subarachnoid haemorrhages were rare among PWH.