ABSTRACT Sub-Neptunes represent the current frontier of exoplanet atmospheric characterization. A proposed subset, Hycean planets, would have liquid water oceans and be potentially habitable, but there are many unanswered questions about their atmospheric dynamics and 3D climate states. To explore such climates in detail, we report a General Circulation Model (GCM) for Hycean worlds, building on a modified version of the ExoCAM GCM. Considering the temperate sub-Neptune K2-18b as a Hycean candidate, we implement GCMs with different surface pressures and albedos. We find dynamical structures similar to those of tidally locked terrestrial planets as ‘slow rotators’ with either one equatorial or twin mid-latitude zonal jets. We see moist convective inhibition that matches high resolution models, although in hotter cases the inhibited zone is subsaturated. When imposing a top-of-the-atmosphere Bond albedo ($A_b$) by modifying the incident stellar flux, we find that the threshold for K2-18b to not enter a runaway greenhouse state is $A_b~\ge ~0.55$ for a 1 bar atmosphere, consistent with previous studies, and $A_b~\ge ~0.8$ for a 5 bar atmosphere. However, a more realistic treatment of the albedo, by modelling scattering within the atmosphere using an enhanced Rayleigh parametrization, leads to lower lapse rates and stronger thermal inversions. We find that 1 bar atmospheres are stable for an albedo of $A_b~\ge ~0.27$, 5 bar atmospheres for $A_b~\ge ~0.35$, and 10 bar atmospheres for $A_b~\ge ~0.48$. Moderate albedos such as these are typical of the Solar system planets and the required scattering is consistent with observational constraints for K2-18b, supporting its plausibility as a Hycean world.