A glass for magnetic recording medium substrate is an amorphous oxide glass. In terms of mol %, SiO2 content ranges from 45 to 68%, Al2O3 from 5 to 20%, total content of SiO2 and Al2O3 60 to 80%, B2O3 from 0 to 5%, MgO from 3 to 28%, CaO from 0 to 18%, total content of BaO and SrO 0 to 2%, total content of alkali earth metal oxides from 12 to 30%, total content of alkali metal oxides from 3.5 to 15%, and at least one kind selected from the group made of Sn oxide and Ce oxide being included, a total content of Sn oxide and Ce oxide ranges from 0.05 to 2.00%, a glass transition temperature ≥625° C., a Young's modulus ≥83 GPa, a specific gravity ≤2.85, and an average linear expansion coefficient at 100 to 300° C.≥48×10−7/° C.