NOVELTY - Extracting alumina and silica from coal solid waste comprises (i) uniformly mixing the coal solid waste with concentrated sulfuric acid to obtain acid solution and curing; (ii) roasting fly ash or gangue powder with reducing agent to obtain reduced calcine and sulfur containing flue gas, and passing sulfur containing flue gas into acid solution; (iii) extracting silicon from reduced calcine using sodium hydroxide solution, filtering to separate silicon extract and aluminous slag; and (iv) extracting aluminous slag using sodium hydroxide solution, filtering, purifying, seeding, and calcining.    USE - The method is useful for extracting alumina and silica from coal solid waste (claimed).    DETAILED DESCRIPTION - Extracting alumina and silica from coal solid waste comprises (i) uniformly mixing the coal solid waste with concentrated sulfuric acid at 120-500 degrees C to obtain acid solution and then curing; (ii) roasting fly ash or gangue powder with reducing agent at 950-1200 degrees C for 0.1-30 minutes to obtain reduced calcine and sulfur containing flue gas, and then passing sulfur containing flue gas into the step (i) acid solution, where the reducing agent is a mixture of pulverized coal, coal gangue, coal gas, natural gas, sulfur or petroleum coke and/or other low value carbon-containing fuel, and the amount of the reducing agent is based on alumina content in fly ash and carbon residual in fly ash; (iii) extracting silicon from reduced calcine using sodium hydroxide solution (sodium oxide concentration is 50-150 g/l), and then filtering to separate silicon extract and aluminous slag, where the volume ratio of reduced calcine and sodium hydroxide solution is 1:3-1:20, the extracting temperature is 50-100 degrees C, extracting time is 30-240 minutes, and the silicon extract solution is useful in producing active silica or calcium silicate; and (iv) extracting step (iii) aluminous slag using sodium hydroxide solution (concentration of sodium oxide is 150-300 g/l), filtering, purifying to obtained sodium aluminate solution, seeding, and then calcining , where the volume ratio of aluminous slag and sodium hydroxide solution is 1:3-1:20, ingredients molecular ratio of alpha k 1-2, adding lime in an amount of 0-15% by mass of aluminous slag, the extracting temperature is 150-300 degrees C, and the extracting time is 15-120 minutes.