The properties of the Li1.5Al0.5Ge1.5(PO4)3 glass-ceramics were modified by the partial substitution of P5+ by Si4+, and the synthesis process is optimized. The thermal behavior of the original Li1.5+хAl0.5Ge1.5SixP3-xO12 (0 ≤ x ≤ 0.5) glasses was investigated using differential scanning calorimetry (DSC), optical dilatometry and heating microscopy. The glass transition temperature (Tg) decreases from 525 to 457 °C with increasing additive content from x = 0 to x = 0.5. Single-phase glass-ceramics with the NASICON-type structure were synthesized up to x = 1, which was confirmed by X-ray diffraction (XRD), Raman and energy-dispersive X-ray (EDX) mapping data. It has been shown that the SiO2 addition has a beneficial effect on the electrical properties of glass-ceramics, crystallized at 700 and 750 °C. However, heat treatment at 820 °C leads to a smaller increase in conductivity. Therefore, Si-containing glass-ceramics should be produced at lower temperatures than pure LAGP, which is 750 °C and correlated with the thermal analysis results. The influence of the SiO2 addition on the bulk and grain boundary conductivity of the Li1.5Al0.5Ge1.5(PO4)3 has been studied in detail. The Li1.52Al0.5Ge1.5Si0.02P2.98O12 glass-ceramics has the highest total ionic conductivity of 4.55·10−4 S/cm at RT and negligible electronic conductivity of 7.5·10−10 S/cm, therefore can be considered as promising solid electrolytes for all-solid-state batteries.