This study reports five types of metal-doped (Co, Cu, Sn, V, and Zr) NASICON-type Li1.3Al0.3Ti1.7(PO4)3 (LATP)/polymer composite solid electrolytes (CSEs) enabling Li4Ti5O12 (LTO) anodes to have high rate capability and excellent cycling performance. The high Li+-conductivity LATP samples are successfully synthesized through a modified sol–gel method followed by thermal calcination. We find that the cation dopants clearly influence the substitution of Al for Ti, with the type of dopant serving as a crucial factor in determining the ionic conductivity and interfacial resistance of the solid electrolyte. The CSE containing poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP), lithium bis(trifluoromethanesulfonyl)imide (LiTFSI), and Sn-LATP shows an ionic conductivity of 1.88 × 10−4 S cm−1 at ambient temperature. The optimum conductivity can be attributed to alterations in the lattice parameters and Li+ transport pathways owing to Sn doping. The solid-state cell equipped with the LTO-supported CSE containing Sn-LATP fillers demonstrates both excellent high rate capability at 5 C (with a capacity retention of 86% compared to the value measured at 0.2 C) and superior cycling stability, maintaining high Coulombic efficiency (>99.0%) over 510 cycles. These findings indicate that the proposed CSE is highly promising for use in solid-state lithium batteries with desirable charge–discharge properties and high durability.