The Coupled Model Intercomparison Project phase 6 (CMIP6) HighResMIP is a new experimental design for global climate model simulations that aims to assess the impact of model horizontal resolution on climate simulation fidelity. We describe a hierarchy of global coupled model resolutions based on the Hadley Centre Global Environment Model 3 – Global Coupled vn 3.1 (HadGEM3-GC3.1) model that ranges from an atmosphere–ocean resolution of 130 km–1∘ to 25 km–1∕12∘, all using the same forcings and initial conditions. In order to make such high-resolution simulations possible, the experiments have a short 30-year spinup, followed by at least century-long simulations with constant forcing to assess drift. We assess the change in model biases as a function of both atmosphere and ocean resolution, together with the effectiveness and robustness of this new experimental design. We find reductions in the biases in top-of-atmosphere radiation components and cloud forcing. There are significant reductions in some common surface climate model biases as resolution is increased, particularly in the Atlantic for sea surface temperature and precipitation, primarily driven by increased ocean resolution. There is also a reduction in drift from the initial conditions both at the surface and in the deeper ocean at higher resolution. Using an eddy-present and eddy-rich ocean resolution enhances the strength of the North Atlantic ocean circulation (boundary currents, overturning circulation and heat transport), while an eddy-present ocean resolution has a considerably reduced Antarctic Circumpolar Current strength. All models have a reasonable representation of El Niño–Southern Oscillation. In general, the biases present after 30 years of simulations do not change character markedly over longer timescales, justifying the experimental design.