The invention belongs to a preparation method of a copolymer of an unsaturated aliphatic compound, more particularly discloses a preparation method of anionic polyacrylamide. The preparation method comprises the following steps of: preparing raw materials for preparation, wherein the raw materials for preparation comprise acrylamide, acrylic acid, sodium hydroxide, potassium sulfate, sodium thiosulfate, ascorbic acid, a molecular weight regulator and water; dissolving the sodium hydroxide in water and neutralizing with the acrylic acid, adding the acrylamide into the neutralized mixed solution to obtain a mixed solution A; then dissolving the sodium thiosulfate, the ascorbic acid and the molecular weight regulator in water to obtain a mixed solution B; dissolving the potassium persulfate in water to obtain a mixed solution C; then adding the mixed solution B into the mixed solution A and finally adding the mixed solution C; and initiating a polymerization reaction at the temperature of 15 to 45 DEG C, insulating heat and naturally heating, pelleting, drying and crushing after the reaction is finished to obtain polyacrylamide powder. The preparation method has the advantages of short reaction time, low preparation cost, less energy consumption, environmental protection and safety, and the like.