There are provided an intermetallic-compound superconductor that is high in superconducting transition temperature, and an alloy superconductor that is high in superconducting transition temperature and excels in malleability and ductility, as well as a method of making such a superconductor with good reproducibility and at a low cost of manufacture. This entirely new intermetallic compound superconductor is made of magnesium (Mg) and beryllium (Be) and has a chemical composition expressed by formula: Mg.sub.1Be.sub.2, has a hexagonal AlB.sub.2 type crystallographic structure and has a superconducting transition temperature (T.sub.c) of 35 K. An alloy containing this intermetallic compound excels in malleability and ductility and constitutes the alloy superconductor having a superconducting transition temperature (T.sub.c) of 35 K and being low in specific resistance for normal conduction at a temperature ranging from the superconducting transition temperature to a room temperature. In the method of manufacture, a Mg containing feedstock powder and a Be containing feedstock powder are mixed together to form a mixture thereof which is, e.g., hot pressed to produce a semiconductor product.