Scale-dependence is a common feature to all effective models of quantum gravity. In this paper, a cosmological model based on the scale-dependent scenario of gravity is presented. It is argued that such models, where the scale-dependence appears as a correction to the classical ΛCDM evolution, have the potential of addressing the tensions between early and late time measurements of H0. After defining criteria to parametrize this tension, we perform a numerical scan over the parameter space of the scale-dependent model, subject to these criteria. In this analysis, it is found that, indeed, the tension can be released.