The present invention relates to rare earth metallurgy, in particular a method for recovering scandium from the red mud byproduct of alumina production. The method includes repulping red mud, sorption leaching scandium therefrom with the use of an ion-exchange sorbing agent to obtain a rich-in-scandium ion exchanger and depleted-in-scandium pulp, desorbing scandium with a solution of sodium hydrocarbonate to obtain a desorbed ion exchanger which is returned to the sorption leaching stage and a solution of industrial reclaim scandium which is transferred to obtain a deposited concentrated scandium, wherein scandium is continuously sorption-leached from red mud pulp in the phosphorous-containing ion exchanger in a countercurrent mode upon direct contact of the pulp with the ion exchanger, scandium is desorbed from the organic phase of the ion exchanger by a solution with a concentration of Na2CO3 of 200-450 g/dm3 to obtain industrial reclaim scandium, from which a scandium concentrate is recovered.