  We theoretically study the quantized anomalous Hall effect (QAHE) in skyrmion
crystal (SkX) without external magnetic field. The emergent magnetic field in
SkX could be gigantic as much as $\sim4000$T when its lattice constant is
$\sim1$nm. The band structure is not flat but has a finite gap in the low
electron-density regime. We also study the conditions to realize the QAHE for
the skyrmion size, carrier density, disorder strength and temperature.
Comparing the SkX and the system under the corresponding uniform magnetic
field, the former is more fragile against the temperature compared with the
latter since the gap is reduced by a factor of $\sim$ 1/5, while they are
almost equally robust against the disorder. Therefore, it is expected that the
QAHE of SkX system is realized even with strong disorder at room temperature
when the electron density of the order of one per a skyrmion.
