The high alkali content of alkaline accelerators has a negative influence on the late strength and durability of concrete. Further, their corrosive nature is harmful to the skin of construction personnel, posing safety concerns. Therefore, the development of alkali-free accelerators has gained interest, especially in shotcrete-based constructions. The production process of aluminum-sulfate-based alkali-free accelerators is simple and less exothermic, with no negative impact on the later strength of concrete, aspects that are widely recognized and very important in construction. However, their high sulfate content may have a significant impact on the durability of concrete; therefore, reducing the sulfate content plays an important role in enhancing the durability of concrete. In this study, an alkali-free liquid accelerator was synthesized by replacing aluminum sulfate with aluminum formate, which effectively reduced the sulfate content. Experiments were performed on concrete samples in which aluminum sulfate was replaced with aluminum formate at different levels. The results showed that the formate and 3CaO·Al2O3 (C3A) of the alkali-free liquid accelerator prepared from aluminum formate form calcium aluminate, similar to the ettringite phase. The formate promoted the dissolution of Ca3SiO5 (C3S), thus accelerating the hydration of concrete. Meanwhile, aluminum ions hydrolyzed by aluminum formate also participated in the reaction, resulting in the dual participation of cations and anions in hydration, leading to a synergistic effect with aluminum sulfate.