Despite the important role of strontium aluminosilicate glasses in various technologies, there is no available phase diagram for this ternary system in the ACerS-NIST Phase Equilibria Diagrams Database. Establishing the liquidus surface (liquidus temperature Tliq and primary devitrification phase) is crucial for glass composition design, because the liquidus temperature is intimately connected with the glass-forming ability of the melt. In this work, we have determined the liquidus surface by X-ray diffraction phase analyses of isothermally reacted samples from powder mixtures of 24 compositions. In the composition range of interest for industrial glasses, Tliq tends to decrease with increasing strontium-to-alumina ratio. We find that cristobalite, mullite, and slawsonite are the dominant devitrification phases for the compositions with high SiO2, SiO2+Al2O3, and SrO contents, respectively. By comparison with the phase diagrams for CaO-Al2O3-SiO2 and MgO-Al2O3-SiO2 systems, we have found that for the highest [RO]/[Al2O3] ratios, Tliq exhibits a minimum value for R = Ca. Based on the phase diagram established here, the composition of glass materials, for example, for liquid crystal display substrates, belonging to the SrO-Al2O3-SiO2 family may be designed with a more exact control of the glass-forming ability by avoiding the regions of high liquidus temperature.