The advantages of all-solid-state batteries in terms of high energy density and improved safety have accelerated the research into durable and reliable solid electrolytes and into scale up of their processing technology. High lithium-ion-conducting Li7La3Zr2O12 (LLZO) ceramic-based solid electrolytes have been intensively studied recently, but their widespread commercial deployment has been constrained due to their fragility and brittleness. In the present study, LLZO ceramic powders have been successfully incorporated into the polyethylene oxide (PEO) polymer by tape casting. The ionic conductivity of the PEO/LLZO composite electrolyte membranes is significantly enhanced at the optimal LLZO concentration of 7.5 wt.% at which the materials exhibits maximum ionic conductivity of 5.5 × 10−4 S·cm−1 at 30 °C. The ionic conductivity enhancement mechanism of the composite electrolyte is revealed by differential scanning calorimetry (DSC), which shows that the LLZO filler represses crystallinity in PEO. Furthermore, as evidence of the advantageous electrochemical properties of the composite electrolyte an all-solid-state battery of LiFePO4/Li fabricated herein delivered a maximum discharge capacity of 150.1 mAh·g−1 at 0.1C, good cycling performance, and excellent rate capability under 60 °C.