  This paper examines a cosmological model of scale-dependent gravity. The
gravitational action is taken to be the Einstein-Hilbert term supplemented with
a cosmological constant, where the couplings, $G_k$ and $\Lambda_k$, run with
the energy scale $k$. % Also, notice that, by construction, our formalism
recovers general relativity when in the limit of constant Newton's coupling. %
Two sub-models based on the scale-dependent cosmological model are confronted
with recent observational data from:
  i) the Hubble parameter $H(z)$,
  ii) distance modulus $\mu(z)$, and iii) baryon acoustic scale evolution as
functions of redshift (BAO). % The viability of the model is discussed,
obtaining the best-fit parameters and the maximum likelihood contours for these
observables. Finally, a joint analysis is performed for $H(z)$+$\mu(z)$+BAO.
