The solid-state lithium batteries (SSLBs) are wide studied owing to its high safety and low cost. However, the poor ionic conductivity of solid electrolyte and low capacity of cathode limit its commercial application. In this paper, nanosized cubic phase Li6.75La3Zr1.75Ta0.25O12 powders is prepared via a simple solution combustion method and used to develop a ceramic-based composite solid electrolyte, which presents high ionic conductivity (1.05 × 10−4 S cm−1 at 25 °C), high lithium ion transference number tLi+ (0.74), wide electrochemical window (4.8 V vs. Li/Li+), excellent heat resistance and electrolyte-electrode interfacial stability. In addition, a high loading (~10.5 mg cm−2) LiNi0.5Co0.2Mn0.3O2 composite cathode with succinonitrile and lithium bis(trifluoromethanesulfonyl)imide as additives is used to fabricate SSLBs, which exhibits a high initial discharge capacity of 146.9 mA h g−1 and good capacity retention of 86.89% after 150 cycles at 0.1 C under 25 °C. The superior performance indicates that solid-state lithium battery assembled with composite solid electrolyte and high loading composite cathode provides a promising choice for the practical development of high-energy-density lithium batteries.