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We investigate what role the SKA neutral hydrogen (HI) intensity mapping (IM)sky survey observation will play in weighing neutrinos in cosmology. We use thesimulated data of the baryon acoustic oscillation (BAO) measurements from theHI IM survey based on SKA1 and SKA2 to do the analysis. For the currentobservations, we use the Planck 2015 cosmic microwave background (CMB)anisotropies observation, the optical BAO measurements, the type Ia supernovae(SN) observation (Pantheon compilation), and the latest $H_0$ measurement. Weconsider three mass ordering cases for massive neutrinos, i.e., the normalhierarchy (NH), inverted hierarchy (IH), and degenerate hierarchy (DH) cases.It is found that the SKA observation can significantly improve the constraintson $\Omega_{\rm m}$ and $H_0$. Compared to the current observation, the SKA1data can improve the constraints on $\Omega_{\rm m}$ by about 33%, and on $H_0$by about 36%; the SKA2 data can improve the constraints on $\Omega_{\rm m}$ byabout 58%, and on $H_0$ by about 66%. It is also found that the SKA observationcan only slightly improve the constraints on $\sum m_\nu$. Compared to thecurrent observation, the SKA1 data can improve the constraints on $\sum m_\nu$by about 4%, 3%, and 10%, for the NH, IH, and DH cases, respectively; the SKA2data can improve the constraints on $\sum m_\nu$ by about 7%, 7%, and 16%, forthe NH, IH, and DH cases, respectively.

Forecast for weighing neutrinos in cosmology with SKA