Polyethylene oxide (PEO)-based solid-state electrolytes are considered ideal for electrolyte materials in solid-state lithium metal batteries (SSLMBs). However, practical applications are hindered by the lower conductivity and poor interfacial stability. Here, we propose a strategy to construct a three-dimensional (3D) fiber network of metal-organic frameworks (MOFs). Composite solid electrolytes (CSEs) with continuous ion transport pathways were fabricated by filling a PEO polymer matrix in fibers containing interconnected MOFs. This 3D fiber network provides a fast Li⁺ transport path and effectively improves the ionic conductivity (1.36 × 10⁻⁴ S·cm⁻¹, 30 °C). In addition, the network of interconnected MOFs not only effectively traps the anions, but also provides sufficient mechanical strength to prevent the growth of Li dendrites. Benefiting from the advantages of structural design, the CSEs stabilize the Li/electrolyte interface and extend the cycle life of the Li-symmetric cells to 3000 h. The assembled SSLMBs exhibit excellent cycling performance at both room and high temperatures. In addition, the constructed pouch cells can provide an areal capacity of 0.62 mA·h·cm⁻², which can still operate under extreme conditions. This work provides a new strategy for the design of CSEs with continuous structure and stable operation of SSLMBs.