Composite electrolytes consisting of polymers and three-dimensional (3D) fillers are considered to be promising electrolytes for solid lithium batteries owing to their virtues of continuous lithium-ion pathways and good mechanical properties. In the present study, an electrolyte with polyethylene oxide–lithium (bis trifluoromethyl) sulfate–succinonitrile (PLS) and frameworks of three-dimensional SiO2 nanofibers (3D SiO2 NFs) was prepared. Taking advantage of the highly conductive interfaces between 3D SiO2 NFs and PLS, the total conductivity of the electrolyte at 30 °C was approximately 9.32 × 10−5 S cm−1. With a thickness of 27 μm and a tensile strength of 7.4 MPa, the electrolyte achieved an area specific resistance of 29.0 Ω cm2. Moreover, such a 3D configuration could homogenize the electrical field, which was beneficial for suppressing dendrite growth. Consequently, Li/LiFePO4 cells assembled with PLS and 3D SiO2 NFs (PLS/3D SiO2 NFs), which delivered an original specific capacity of 167.9 mAh g−1, only suffered 3.28% capacity degradation after 100 cycles. In particular, these cells automatically shut down when PLS was decomposed above 400 °C, and the electrodes were separated by the solid framework of 3D SiO2 NFs. Therefore, the solid lithium batteries based on composite electrolytes reported here offer high safety at elevated temperatures.