In this work, genetic connections (GC) of the small meteor shower ρ-Geminids with near-Earth objects (NEOs) of the Apollo group were studied using the author’s multi-parameter method. The multiparameter method for determining GC of meteor showers with probable parent bodies is based on the use of a set of criteria for identifying orbits, such as: D-criterion by Drummond, Kholshevnikov’s metric, Tisserand’s parameter, μ and ν quasi-stationary parameters of the restricted three-body problem, longitude of perihelion π of meteor orbit. The method of identifying meteoroids with asteroids involves computational procedures and the calculation of critical values for each of the criteria used, which increases the reliability of finding the GC for the objects under study. The catalogues of meteor orbits: Meteoroid Orbit Database v3.0, CAMS and EDMOND 5 v.04 of the European Meteor Network were used as source material in the work.