© 2020 Elsevier B.V. To clarify the relationship between the glass-forming ability (GFA) and local atomic structure of Pd-based metallic glasses, the structures of an amorphous Pd40Cu40P20 (PCP) were investigated using the same methods as for Pd40Ni40P20 (PNP) metallic glass, i.e., by a combination of anomalous X-ray scattering, X-ray and neutron diffraction, and reverse Monte Carlo modeling. From the comparison between the results of PNP with an excellent GFA and the PCP with a worse GFA, important features characteristic to the GFA are found in the hyper-ordered structures. Firstly, the compositional inhomogeneity of Cu in PCP is larger than Ni in PNP. Secondly, a Voronoi tessellation reveals that icosahedral arrangements are found with considerable probability around the Ni atoms in PNP, while a less existence around the Cu atoms in PCP. Thirdly, a persistent homology (PH) analysis shows smaller intermediate-size Cu PH rings in PCP than Ni PH rings in PNP.