The family of (Sr,Mg)-doped $LaGaO_3$ compounds, which exhibit high ionic conductivity at $600-800^{circ}C$ over a wide range of oxygen partial pressure, appears to be promising as the electrolyte for intermediate temperature solid oxide fuel cells. Conventional synthesis routes of (Sr,Mg)-doped $LaGaO_3$ compounds based on solid state reaction have some problems such as the formation of impurity phases, long sintering time and Ga loss during high temperature sintering. Phase stability problem especially, the formation of additional phases at the grain boundary is detrimental to the electrical properties of the electrolyte. From this point of view, we focused to synthesize single phase (Sr,Mg)-doped $LaGaO_3$ electrolyte at the stage of powder synthesis and to apply relatively low heat-treatment temperature using novel synthesis route based on combustion method. The synthesized powder and sintered bulk electrolytes were characterized by XRD, TG-DTA, FT-IR and SEM. AC impedance spectroscopy was used to characterize the electrical transport properties of the electrolyte with the consideration of the contribution of the bulk lattice and grain boundary to the total conductivity. Finally, relationship between synthesis condition and electrical properties of the (Sr, Mg)-doped $LaGaO_3$ electrolytes was discussed with the consideration of phase analysis results.