Arctic precipitation is projected to increase more rapidly than the global mean in warming climates. However, warming-induced changes in the variability of Arctic precipitation, which are related to surface evaporation and poleward moisture transport (PMT), are currently largely unknown. This study compares the precipitation variability in different quasi-equilibrium climates simulated by a global climate model (EC-Earth) and studies the underlying mechanisms. Five quasi-equilibrium simulations of 400 years length forced with a broad range of CO2 concentrations (0.25, 0.5, 1, 2, and 4 times the current global mean) were analyzed. PMT is the dominant source of Arctic precipitation variability in colder climates when the ocean in the Arctic basin is completely covered by sea ice year-round. Arctic precipitation variability increases from colder to warmer climates, primarily in summer. In summer, the increasingly stronger relation between Arctic sea level pressure variability and precipitation variability toward warmer climates enhances variability. In winter, the severe increase in mean precipitation (due to enhanced evaporation) exerts a comparatively small increase in variability, and precipitation variability is modulated by both PMT and evaporation, which oppose each other as they both affect the vertical and meridional moisture gradients.