Introducing a small dose of an electrolyte additive into solid polymer electrolytes (SPEs) is an appealing strategy for improving the quality of the solid-electrolyte-interphase (SEI) layer formed on the lithium metal (Li°) anode, thereby extending the cycling life of solid-state lithium metal batteries (SSLMBs). In this work, we report a new type of SPEs comprising a low-cost, fluorine-free salt, lithium tricyanomethanide, as the main conducting salt and a fluorinated salt, lithium bis(fluorosulfonyl)imide (LiFSI), as the electrolyte additive for enhancing the performance of SPE-based SSLMBs. Our results demonstrate that a homogeneous and stable SEI layer is readily formed on the surface of the Li° electrode through the preferential reductive decomposition of LiFSI, and consequently, the cycle stabilities of Li°||Li° and Li°||LiFePO4 cells are significantly improved after the incorporation of LiFSI as an additive. The intriguing chemistry of the salt anion revealed in this work may expedite the large-scale implementation of SSLMBs in the near future.