Tightly connected interface between individual active material particles and solid state electrolytes with large surface area is strongly required for the achievement of high-performance all-solid-state Li ion rechargeable batteries (ASS-LIBs). In this work, we performed flux growth of Li₃BO₃/Li_6.75La₃Zr_1.75Nb_0.25O₁₂ composite electrolytes and LiCoO₂/Li₃BO₃/Li_6.75La₃Zr_1.75Nb_0.25O₁₂ composites electrodes under various composition rate at 1000 ^oC.Powder XRD profiles and cross-sectional SEM images revealed that individual LiCoO₂ and Li_6.75La₃Zr_1.75Nb_0.25O₁₂ single crystals were homogeneously dispersed in amorphous Li₃BO₃ matrix without formation of any sub-phase at the interphase even though the crystal growth process was performed under 1000 ^oC for 5h. The each crystals size and the relative density of the composite was increased as increasing time and temperature. The relative density was maximally 92%. Indicating that small volumetric amount of Li₃BO₃ plays a key rule for insulating the direct contact of LiCoO₂ with Li_6.75La₃Zr_1.75Nb_0.25O₁₂ as well as for assisting the enhancement of relative density of composites relied on liquid-state sintering principle. The Li ion conductivity of the composite electrolyte with ca. 700 mm thick was 2.0×10^-4 S/cm at room temperature, and the composite electrodes with ca. 700 mm thick was 1.1×10^-4 S/cm, as evaluated by AC-impedance spectroscopy. We believe that the flux co-growth of LiCoO₂ single crystals and Li_6.75La₃Zr_1.75Nb_0.25O₁₂ single crystals in a molten Li₃BO₃ glass resulted in the formation of smart interface which provide efficient Li⁺ transfer. We also characterized their all-solid-state LIBs properties.