  We investigate what role the SKA neutral hydrogen (HI) intensity mapping (IM)
sky survey observation will play in weighing neutrinos in cosmology. We use the
simulated data of the baryon acoustic oscillation (BAO) measurements from the
HI IM survey based on SKA1 and SKA2 to do the analysis. For the current
observations, 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. We
consider three mass ordering cases for massive neutrinos, i.e., the normal
hierarchy (NH), inverted hierarchy (IH), and degenerate hierarchy (DH) cases.
It is found that the SKA observation can significantly improve the constraints
on $\Omega_{\rm m}$ and $H_0$. Compared to the current observation, the SKA1
data 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 $\Omega_{\rm m}$ by
about 58%, and on $H_0$ by about 66%. It is also found that the SKA observation
can only slightly improve the constraints on $\sum m_\nu$. Compared to the
current 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 SKA2
data can improve the constraints on $\sum m_\nu$ by about 7%, 7%, and 16%, for
the NH, IH, and DH cases, respectively.
