The invention discloses a three-stage distillation device for purifying alkali metal and a method ofpurifying alkali metal. Due to the adoption of the three-stage distillation device, the problem that the alkali metal liquid rolls, takes the micro particles and the impurities in the liquid out of the distillation device and causes influence on the purity of distilled cesium or rubidium when the alkali metal rapidly gasifies and jumps because the bottom of the alkali metal is heated during heating and distilling outside a glass distillation device filled with the alkali metal cesium or rubidium in the purification process of the alkali metal can be thoroughly overcome; except a mechanical pump, a complete set of device is designed by glass tubes, so that the manufacture cost is reduced; meanwhile, the distillation process is clearly visible and can be adjusted according to the observation situation at any time; a spherical coldtrap and an oil-free spherical glass valve are additionally arranged between a high vacuum air extraction system and a three-stage heating and distilling system; the pollution of the alkali metal cesium or rubidium to the high vacuum air extraction system is reduced; and the service life of the high vacuum air extraction system is prolonged.