This study reports cobalt- and copper-doped NASICON-type Li1.5Al0.5Ti1.7(PO4)3 (LATP) polymer composite solid-state electrolytes (CSEs) enabling Li4Ti5O12 (LTO) electrode with high-rate capability and excellent cyclic performance for solid-state lithium batteries. The fast Li+ conductor of Co- and Cu-doped LATP powders was successfully synthesized through a modified sol-gel method followed by thermal calcination. The equivalent series resistance as the linear decreasing function of the dopant concentration can be viewed, whereas the ionic conductivity showed an increasing function of the dopant amount. This reveals that the dopant concentration plays a positive role in facilitating the ionic conduction, and the ionic conductivity achieves as high as 3.18 × 10−4 S cm−1 (Co-doping) and 2.99 × 10−4 S cm−1 (Cu-doping) at ambient temperature. The changes in lattice characteristics and microstructure that the Co and Cu doping rely on are responsible for the elevated conductivity. The solid-state cell equipped with LTO-supported CSEs demonstrated not only high-rate capability at 5C (with a capacity retention of 84.6 % compared to the original capacity at 0.2C), but also superior cyclic stability with excellent Coulombic efficiency (> 99.2 %) over 425 cycles using Co- and Cu-doped LATP ceramics. With the aid of fast Li+ NASICON-type ceramics, the CSEs establish a conductive ionic pathway that facilitates Li+ ionic transport within the electrolyte while reducing the interfacial electrolyte/electrode resistance in solid-state cells (Li||CSE||LTO).