Inspired by an exponential [Formula: see text] gravity model studied in the literature, in this work we introduce a new and viable [Formula: see text] gravity model, which can be represented as a perturbation of [Formula: see text]CDM. Typically, within the realm of [Formula: see text] gravity, the customary approach to investigate cosmological evolution involves employing a parametrization of the Hubble expansion rate in terms of the redshift, [Formula: see text], among other strategies. In this work, we have implemented a different strategy, deriving an analytical approximation for [Formula: see text], from which we deduce approximated analytical expressions for the parameters [Formula: see text], [Formula: see text] and [Formula: see text], as well as the deceleration parameter q. In order to verify the viability of this approximate analytical solution, we examined the behavior of these parameters in the late-time regime, in terms of the free parameter of the model, b. We find that for [Formula: see text], [Formula: see text] shows a quintessence-like behavior, while for [Formula: see text], it shows a phantom-like behavior. However, regardless of the sign of b, [Formula: see text] exhibits a quintessence-like behavior. Furthermore, it has been deduced that as the magnitude of the parameter b increases, the present model deviates progressively from [Formula: see text]CDM. We have also performed a Markov Chain Monte Carlo statistical analysis to test the model predictions with the Hubble parameter, the Pantheon supernova (SN) observational data and the combination of those samples, obtaining constraints on the parameters of the model and the current values of the Hubble parameter and the matter density. Our findings indicate that this [Formula: see text] gravity model is indeed a viable candidate for describing the late-time evolution of the Universe at the background level.