  We investigate Hawking radiation in the novel $4D$ Einstein-Gauss-Bonnet
gravity which is recently formulated by Glavan and Lin [Phys. Rev. Lett. 124,
081301 (2020)]. We first find the constraints on $\alpha$ and $\Lambda$ to
retain a dS black hole in the spacetime. Both the greybody factor and the power
spectra of the Hawking radiation of the massless scalar are studied for the
full range of various parameters including the GB coupling constant $\alpha$,
the cosmological constant $\Lambda$ and the constant related to the scalar
$\xi$ numerically. In particular, we find the greybody factor is larger for a
negative $\alpha$ than the case for $\alpha\ge0$. While, the power spectra of
the Hawking radiation is higher for a allowed negative $\alpha$ than others
with non-negative $\alpha$. The reason is that the temperature of the black
hole would be very high when $\alpha<0$, even when $\alpha$ approaches the
lower bound, the temperature would be arbitrary high.
