Abstract　 　　
　 Giant flares on soft gamma-ray repeaters that are thought to take place on magnetars release enormous energy in a short time interval. Their power can be explained by the catastrophic instability occurring in the relevant magnetic configuration and the consequent magnetic reconnection. By analogy with the coronal mass ejection (CME) events on the Sun, we propose a magnetohydrodynamic (MHD) model for the magnetar giant flares. In this model, the rotation and/or the displacement of the crust cause the field to twist and deform, leading to the flux rope formation in the magnetosphere and the energy accumulation in the related configuration. When the energy and helicity stored in the configuration reach a threshold, the system loses its equilibrium, the flux rope is ejected outward in a catastrophic way and the magnetic reconnection helps the catastrophe develop to a plausible eruption. By taking SGR 1806-20 as an example, we calculate the free magnetic energy released in such an eruptive process and find that it is more than 10^47 ergs, which is enough to power a giant flare. The released free magnetic energy is converted into the radiative energy, the kinetic energy and the gravitational energy of the flux rope. We calculated the light curves of the eruptive processes for the giant flares of SGR 1806-20, SGR 0526-66 and SGR 1900+14, and compared them with the observational data. The calculated light curves are in good agreement with the observed light curves of giant flares.