  Recently, the emergence of cosmological tension has raised doubts about the
consistency of the $\Lambda$CDM model. In order to constrain the neutrino mass
within a consistent cosmological framework, we investigate three massive
neutrinos with normal hierarchy (NH) and inverted hierarchy (IH) in both the
axion-like EDE (Axi-EDE) model and the AdS-EDE model. We use the joint datasets
including cosmic microwave background (CMB) power spectrum from Planck 2018,
Pantheon of type Ia supernova, baryon acoustic oscillation (BAO) and $H_0$ data
from SH0ES. For the $\nu$Axi-EDE model, we obtain $\sum m_{\nu,\mathrm{NH}} <
0.152$ eV and $\sum m_{\nu,\mathrm{IH}} < 0.178$ eV, while for the $\nu$AdS-EDE
model, we find $\sum m_{\nu,\mathrm{NH}} < 0.135$ eV and $\sum
m_{\nu,\mathrm{IH}} < 0.167$ eV. Our results exhibit a preference for the
normal hierarchy in both the $\nu$Axi-EDE model and the $\nu$AdS-EDE model.
