ABSTRACT The amount of mass lost by stars during the red-giant branch (RGB) phase is one of the main parameters to understand and correctly model the late stages of stellar evolution. Nevertheless, a fully comprehensive knowledge of the RGB mass-loss is still missing. Galactic Globular Clusters (GCs) are ideal targets to derive empirical formulations of mass-loss, but the presence of multiple populations with different chemical compositions has been a major challenge to constrain stellar masses and RGB mass-losses. Recent work has disentangled the distinct stellar populations along the RGB and the horizontal branch (HB) of 46 GCs, thus providing the possibility to estimate the RGB mass-loss of each stellar population. The mass-losses inferred for the stellar populations with pristine chemical composition (called first-generation or 1G stars) tightly correlate with cluster metallicity. This finding allows us to derive an empirical RGB mass-loss law for 1G stars. In this paper, we investigate seven GCs with no evidence of multiple populations and derive the RGB mass-loss by means of high-precision Hubble-Space Telescope photometry and accurate synthetic photometry. We find a cluster-to-cluster variation in the mass-loss ranging from ∼0.1 to ∼0.3 M⊙. The RGB mass-loss of simple-population GCs correlates with the metallicity of the host cluster. The discovery that simple-population GCs and 1G stars of multiple population GCs follow similar mass-loss versus metallicity relations suggests that the resulting mass-loss law is a standard outcome of stellar evolution.