The solid-electrolyte interphase (SEI) formed through the reductive decomposition of solvent molecules plays a crucial role in the stability and capability of a lithium-ion battery (LIB). Here we investigated the effects of adding vinylene carbonate (VC) to ethylene carbonate (EC) solvent, a typical electrolyte in LIBs, on the reductive decomposition. We focused on both thermodynamics and kinetics of the possible processes and used density functional theory-based molecular dynamics with explicit solvent and Blue-moon ensemble technique for the free energy change. We considered Li+ in only EC solvent (EC system) and in EC solvent with a VC additive (EC/VC system) to elucidate the additive effects. In addition to clarifying the equilibrium properties, we evaluated the free energy changes along several EC or VC decomposition pathways under one-electron (1e) reduction condition. Two-electron (2e) reduction and attacks of anion radicals to intact molecules were also examined. The present results completely reproduce the gaseous products observed in the experiments. We also found a new mechanism involving the VC additive: the VC additive preferentially reacts with the EC anion radical to suppress the 2e reduction of EC and enhance the initial SEI formation, contrary to the conventional scenario in which VC additive is sacrificially reduced and its radical oligomerization becomes the source of SEI. Because our mechanism needs only 1e reduction, the irreversible capacity at the SEI formation will decrease, which is also consistent with the experimental observations. These results reveal the primary role of VC additive in the EC solvent.