Aviation makes a significant contribution to anthropogenic climate forcing. The impacts arise from emissions of greenhouse gases, aerosols and nitrogen oxides, and from changes in cloudiness in the upper troposphere. An important but poorly understood component of this forcing is caused by ‘contrail cirrus’—a type of cloud that consist of young line-shaped contrails and the older irregularly shaped contrails that arise from them. Here we use a global climate model that captures the whole life cycle of these man-made clouds to simulate their global coverage, as well as the changes in natural cloudiness that they induce. We show that the radiative forcing associated with contrail cirrus as a whole is about nine times larger than that from line-shaped contrails alone. We also find that contrail cirrus cause a significant decrease in natural cloudiness, which partly offsets their warming effect. Nevertheless, net radiative forcing due to contrail cirrus remains the largest single radiative-forcing component associated with aviation. Our findings regarding global radiative forcing by contrail cirrus will allow their effects to be included in studies assessing the impacts of aviation on climate and appropriate mitigation options.