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In this work, we investigate the constraints on the total neutrino mass inthe scenario of vacuum energy interacting with cold dark matter (abbreviated asI$\Lambda$CDM) by using the latest cosmological observations. We consider fourtypical interaction forms, i.e., $Q=\beta H \rho_{\rm de}$, $Q=\beta H\rho_{\rm c}$, $Q=\beta H_{0} \rho_{\rm de}$, and $Q=\beta H_{0} \rho_{\rm c}$,in the I$\Lambda$CDM scenario. To avoid the large-scale instability problem ininteracting dark energy models, we employ the extended parameterizedpost-Friedmann method for interacting dark energy to calculate the perturbationevolution of dark energy in these models. The observational data used in thiswork include the cosmic microwave background (CMB) measurements from the Planck2018 data release, the baryon acoustic oscillation (BAO) data, the type Iasupernovae (SN) observation (Pantheon compilation), and the 2019 local distanceladder measurement of the Hubble constant $H_{0}$ from the Hubble SpaceTelescope. We find that, compared with those in the $\Lambda$CDM+$\sum m_{\nu}$model, the constrains on $\sum m_{\nu}$ are looser in the fourI$\Lambda$CDM+$\sum m_{\nu}$ models. When considering the three masshierarchies of neutrinos, the constraints on $\sum m_{\nu}$ are tightest in thedegenerate hierarchy case and loosest in the inverted hierarchy case. Inaddition, in the four I$\Lambda$CDM+$\sum m_{\nu}$ models, the values ofcoupling parameter $\beta$ are larger using the CMB+BAO+SN+$H_{0}$ datacombination than that using the CMB+BAO+SN data combination, and $\beta>0$ isfavored at more than 1$\sigma$ level when using CMB+BAO+SN+$H_{0}$ datacombination. The issue of the $H_{0}$ tension is also discussed in this paper.We find that, compared with the $\Lambda$CDM+$\sum m_{\nu}$ model, the $H_{0}$tension can be alleviated in the I$\Lambda$CDM+$\sum m_{\nu}$ model to someextent.

Constraints on neutrino mass in the scenario of vacuum energy interacting with cold dark matter after Planck 2018