An Li1.3Al0.3SnxTi1.7−x(PO4)3 (LATP-xSn) ceramic solid electrolyte was prepared by Sn doping via a solid phase method. The results showed that adding an Sn dopant with a larger ionic radius in a concentration of x = 0.35 enabled one to equivalently substitute Ti sites in the LATP crystal structure to the maximum extent. The uniform Sn doping could produce a stable LATP structure with small grain size and improved relative density. The lattice distortion induced by Sn doping also modified the transport channels of Li ions, which promoted the increase of ionic conductivity from 5.05 × 10−5 to 4.71 × 10−4 S/cm at room temperature. The SPE/LATP-0.35Sn/SPE composite solid electrolyte with a sandwich structure was prepared by coating, which had a high ionic conductivity of 5.9 × 10−5 S/cm at room temperature, a wide electrochemical window of 4.66 V vs. Li/Li+, and a good lithium-ion migration number of 0.38. The Li||Li symmetric battery test results revealed that the composite solid electrolyte could stably perform for 500 h at 60 °C under the current density of 0.2 mA/cm2, indicating its good interface stability with metallic lithium. Moreover, the analysis of the all-solid-state LiFePO4||SPE/LATP-0.35Sn/SPE||Li battery showed that the composite solid electrolyte had good cycling stability and rate performance. Under the conditions of 60 °C and 0.2 C, stable accumulation up to 200 cycles was achieved at a capacity retention ratio of 90.5% and a coulombic efficiency of about 100% after cycling test.