The estimation of the main parameters of star clusters is significant in astrophysical studies. The most important aspect of using the Gaia DR2 survey lies in the positions, parallax, and proper motions of cluster stars with homogeneous photometry that make the membership probability determine with high accuracy. In this respect, depending on Gaia DR2 database, an analysis of the open star cluster Melotte 72 is taking place here. It is located at a distance of 2345+/-108 pc with an age of 1.0+/-0.5 Gyr. In studying the radial density profile, the radius is found to be 5.0+/-0.15 arcmin. The reddening, the luminosity and mass functions, the total mass of the cluster, and the galactic geometrical distances (X_Sun, Y_Sun, Z_Sun), and the distance from the galactic center (R_g ) have been estimated as well. Our study has shown a dynamical relaxation behavior of Melotte 72.
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