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We investigate the impacts of dark energy on constraining massive(active/sterile) neutrinos in interacting dark energy (IDE) models by using thecurrent observations. We employ two typical IDE models, the interacting $w$cold dark matter (I$w$CDM) model and the interacting holographic dark energy(IHDE) model, to make an analysis. To avoid large-scale instability, we use theparameterized post-Friedmann approach to calculate the cosmologicalperturbations in the IDE models. The cosmological observational data used inthis work include the Planck cosmic microwave background (CMB) anisotropiesdata, the baryon acoustic oscillation data, the type Ia supernovae data, thedirect measurement of the Hubble constant, the weak lensing data, theredshift-space distortion data, and the CMB lensing data. We find that the darkenergy properties could influence the constraint limits of active neutrino massand sterile neutrino parameters in the IDE models. We also find that the darkenergy properties could influence the constraints on the coupling strengthparameter $\beta$, and a positive coupling constant, $\beta>0$, can be detectedat the $2.5\sigma$ statistical significance for the IHDE+$\nu_s$ model by usingthe all-data combination. In addition, we also discuss the "Hubble tension"issue in these scenarios. We find that the $H_0$ tension can be effectivelyrelieved by considering massive sterile neutrinos, and in particular in theIHDE+$\nu_s$ model the $H_0$ tension can be reduced to be at the $1.28\sigma$level.

Constraints on active and sterile neutrinos in an interacting dark energy cosmology