Provided is a glass for magnetic recording rnedium substrate, which is an amorphous oxide glass, wherein, in terms of mol7o, an SiOz content ranges from 45 to 680/o; an AlzOr content ranges from 5 to 20o/o; a total content of SiOz and AlzOl ranges from 60 to 80o/r; a BzO: content ranges from 0 to 5o/o; an MgO content ranges from 3 to 28o/o; a CaO content ranges from 0 to I8%o; a total content of BaO and SrO ranges from 0 to 2o/o; a total content of alkali earth metal oxides ranges from 12 to 30o/o; a total content of alkali metal oxides ranges fi'om 3.5 to l5o/o; and at least one kind selected fi'orn the group consisting of Sn oxide and Ce oxide being included, a total content of Sn oxide and Ce oxide ranges from 0.05 to 2.00Yo, a glass transition temperature is equal to or higher than 625"C; a Young's modulus is equal to or more than 83 GPa; a specific gravity is equal to or less than 2.85; and an average linear expansion coeffrcient at 100 to 300oC is equal to or more than 48x l0'7 P