The invention discloses a polymeric aluminum sulfate synthesis method and discloses a preparation method of a novel alkali-free liquid accelerator based on synthesis of polymeric aluminum sulfate. According to the alkali-free accelerator, an aluminum sulfate solution is neutralized by ammonia water, active aluminum hydroxide gel is prepared, active aluminum hydroxide is filtered, dried and ground into powder, then the aluminum sulfate solution is added, and the polymeric aluminum sulfate is prepared. The alkali-free accelerator comprises, in percentage, 45%-55% of the polymeric aluminum sulfate, 0%-5% of inorganic acid, 0%-2% of a stabilizer, 0%-2% of an organic early strength agent, 0%-2% of an organic tackifier and the balance of water. The cement setting time and the colloidal mortar strength of the accelerator can meet the requirement of first-class accelerators for JC477-2005 sprayed concrete under the condition of the lower mixing amount, and meanwhile, the accelerator is an alkali-free liquid accelerator and can effectively avoid adverse effects caused by excessively high alkali content. The cement types of the accelerator have good adaptability.