The invention discloses a method for removing iron, aluminum and silicon from a nickel-cobalt-manganese-copper solution under normal pressure. The method comprises the following steps that 1) a rough nickel-cobalt-manganese-copper raw material is taken and mixed with water to form slurry, then acid and a reducing agent are added for leaching, the pH value at the leaching end point is smaller than or equal to 2.5, and the Fe<2+> content is controlled to be proper; (2) after the leaching slurry is subjected to dense separation, supernate and a precipitator are added, in a parallel flow mode, into liquid which contains nickel, cobalt, manganese and copper without iron, aluminum and silicon at the temperature of 70-100 DEG C, and heat preservation is conducted, wherein the precipitator is a rough nickel-cobalt-manganese-copper raw material with the solid content being 1-50%, and the pH value of the liquid without iron, aluminum and silicon ranges from 3.0 to 4.0; and 3) the slurry is subjected to solid-liquid separation, filtrate is as an extraction stock solution, water is added into removed iron-aluminum-silicon slag and leaching slag to prepare slurry with the solid content being smaller than or equal to 50%, acid is added to regulate the pH value to 2.0-3.5, a reducing agent is added to enable the Fe<2+> concentration to be greater than or equal to 0.1g/L, the removed iron-aluminum-silicon slag and the filtrate are obtained after solid-liquid separation, and the filtrate is fed to a leaching section for leaching raw materials. According to the method, auxiliary materials and hazardous chemicals do not need to be used for removing iron, aluminum and silicon, other elements are not introduced either, the purposes of lowering the cost of the auxiliary materials and the salinity of wastewater are achieved, and the sewage treatment pressure is lowered.