MGCosmoPop implements a hierarchical Bayesian inference method for constraining the background cosmological history, in particular the Hubble constant, together with modified gravitational-wave propagation and binary black holes population models (mass, redshift and spin distributions) with gravitational-wave data. It includes support for loading and analyzing data from the GWTC-3 catalog as well as for generating injections to evaluate selection effects, and features a module to run in parallel on clusters.