We investigate how dark energy properties impact the cosmological limits on the total mass of active neutrinos. We consider two typical, simple dark energy models (that have only one more additional parameter than LambdaCDM ), i.e., the sub(w) CDM model and the holographic dark energy (HDE) model, as examples, to make an analysis. In the cosmological fits, we use the Planck 2015 temperature and polarization data, in combination with other low-redshift observations, including the baryon acoustic oscillations, type Ia supernovae, and Hubble constant measurement, as well as the Planck lensing measurements. We find that, once dynamical dark energy is considered, the degeneracy between Sigmam sub(nu) and H 0 will be changed, i.e., in the LambdaCDM model, Sigmam sub(nu) is anticorrelated with H sub(0), but in the wCDM and HDE models, Sigmam sub(nu) becomes positively correlated with H 0 . Compared to LambdaCDM , in the wCDM model the limit on Sigmam nu becomes much looser, but in the HDE model the limit becomes much tighter. In the HDE model, we obtain Sigmam sub(nu)<0.113eV (95% C.L.) with the combined data sets, which is perhaps the most stringent upper limit by far on neutrino mass. Thus, our result in the HDE model is nearly ready to diagnose the neutrino mass hierarchy with the current cosmological observations.