We present a new cloud scheme for the ECHAM‐HAM global climate model (GCM) that includes prognostic cloud fraction and allows for subsaturation and supersaturation with respect to ice separately in the cloud‐free and cloudy air. Stratiform clouds form by convective detrainment, turbulent vertical diffusion, and large‐scale ascent. For each process, the corresponding cloud fraction is calculated, and the individual updraft velocities are used to determine cloud droplet/ice crystal number concentrations. Further, convective condensate is always detrained as supercooled cloud droplets at mixed‐phase temperatures (between 235 and 273 K), and convectively detrained ice crystal number concentrations are calculated based on the updraft velocity. Finally, the new scheme explicitly calculates condensation/evaporation and deposition/sublimation rates for phase‐change calculations. The new cloud scheme simulates a reasonable present‐day climate, reduces the previously overestimated cirrus cloud fraction, and in general improves the simulation of ice clouds. The model simulates the observed in‐cloud supersaturation for cirrus clouds, and it allows for a better representation of the tropical to extra‐tropical ratio of the longwave cloud radiative effect. Further, the ice water path, the ice crystal number concentrations, and the supercooled liquid fractions in mixed‐phase clouds agree better with observations in the new model than in the reference model. Ice crystal formation is dominated by the liquid‐origin processes of convective detrainment and homogeneous freezing of cloud droplets. The simulated ice clouds strongly depend on model tuning choices, in particular, the enhancement of the aggregation rate of ice crystals. Plain Language Summary This paper describes a new cloud scheme for the global climate model ECHAM‐HAM that better represents the ice cloud formation processes. It calculates the formation of clouds by convection, turbulent vertical diffusion, and large‐scale ascent. For each cloud formation process, the scheme calculates the cloud volume and the number concentration and size of cloud droplets and ice crystals. Further, it calculates how cloud droplets and ice crystals grow with time until they are large enough to form precipitation and are removed from the cloud. We show how the introduction of new formulations of the cloud processes affects the simulated clouds. The new ice cloud fraction compares better to satellite observations. In‐cloud properties including ice crystal number concentrations, the fraction of supercooled liquid clouds, and the radiative effects of clouds are also compared to observations. We conclude that the new cloud scheme better captures the observed properties of ice clouds and improves our capability to simulate and understand ice clouds. Key Points A new cloud scheme with prognostic, process‐based cloud fraction and in‐cloud water vapor was developed for ECHAM‐HAM The new cloud scheme is stable within the GCM and improves the simulation of ice clouds