A metal, or an alloy, can often exist in more than one crystal structure. The face-centred-cubic and body-centred-cubic forms of iron (or steel) are a familiar example of such polymorphism. When metallic materials are made in the amorphous form, is a parallel 'polyamorphism' possible? So far, polyamorphic phase transitions in the glassy state have been observed only in glasses involving directional and open (such as tetrahedral) coordination environments. Here, we report an in situ X-ray diffraction observation of a pressure-induced transition between two distinct amorphous polymorphs in a Ce(55)Al(45) metallic glass. The large density difference observed between the two polyamorphs is attributed to their different electronic and atomic structures, in particular the bond shortening revealed by ab initio modelling of the effects of f-electron delocalization. This discovery offers a new perspective of the amorphous state of metals, and has implications for understanding the structure, evolution and properties of metallic glasses and related liquids. Our work also opens a new avenue towards technologically useful amorphous alloys that are compositionally identical but with different thermodynamic, functional and rheological properties due to different bonding and structural characteristics.