The Arctic (north of 67°N) has been warming up much faster than the rest of the world in recent observations and model simulations with increasing greenhouse gases (GHGs), a phenomenon known as the Arctic amplification (AA). Many mechanisms have been proposed to explain the AA, including a central role by sea-ice loss, reduced outgoing longwave (LW) radiation, increased downward LW heating due to increased water vapor and clouds, increased poleward energy transport, and other processes. However, their relative importance is still under debate. Through analyses of simulations by multiple coupled climate models from 1900-2300 under historical and future GHG emissions and simulations by a fully coupled model with and without fixed Arctic sea-ice cover in calculating surface fluxes under 1%/year CO₂ increase, we found that large AA occurs only from October to April and only over areas with significant sea-ice loss. AA largely disappears when Arctic sea ice is fixed or melts away. Decades with larger AA are associated with larger sea-ice loss, and models with bigger sea-ice loss produce larger AA. Increased LW radiation and latent and sensible heat from the newly opened Arctic waters enhance warming and cause AA; whereas water vapor feedback and increased downward LW radiation can only modulate the AA induced by sea-ice loss or indirectly contribute to AA by melting sea-ice. We conclude that sea-ice loss is necessary for the existence of large AA and that models need to simulate Arctic sea ice realistically in order to correctly simulate Arctic warming under increasing GHGs.