The invention relates to a technology for purifying scandium, titanium and vanadium from an acid solution step by step. According to the technology, the acid solution obtained by leaching red mud through sulfuric acid is subjected to three-time extraction work, and an extraction organic phase is composed of a P507 extraction agent, a TBP synergist and sulfonated kerosene; in the first-time extraction process, the acid solution is directly subjected to scandium extraction and enrichment without pH value adjustment, after two-phase separation, a scandium-enriched organic phase and a titanium and vanadium containing solution are obtained, the scandium-enriched organic phase is subjected to sulfuric acid scrubbing and reverse extraction of sodium hydroxide, and scandium-enriched liquid is obtained; after the titanium and vanadium containing solution is subjected to pH value adjustment, the second-time extraction work is conducted for enrichment and separation of titanium, after two-phase separation, a titanium-enriched organic phase and a vanadium-containing solution are obtained, and after the titanium-enriched organic phase is subjected to sulfuric acid scrubbing and reverse extraction of hydrofluoric acid, titanium-enriched liquid and the vanadium-containing solution are obtained; and after the vanadium-containing solution is subjected to pH value adjustment and reducing treatment, the third-time extraction is conducted, and after two-phase separation, a vanadium-enriched organic phase and raffinate are obtained. The technology has the beneficial effects that the separation efficiency is high, the enrichment multiple is large, the technology is simple, and the number of the kinds of extraction agents is small.