  We propose to realize quantum anomalous Hall effect (QAHE) in two-dimensional
antiferromagnetic topological insulators. We consider antiferromagnetic
MnBi$_2$Te$_4$ as a concrete example. In contrast to the even-layer A-type
antiferromagnetic MnBi$_2$Te$_4$ that has zero Chern number due to the combined
parity-time ($\mathcal{PT}$) symmetry, the system can host a nonzero Chern
number by breaking this symmetry. We show that by controlling the
antiferromagnetic spin configuration, for example, down/up/up/down, to break
$\mathcal{PT}$ symmetry, tetralayer antiferromagnetic MnBi$_2$Te$_4$ can
realize QAHE with Chern number $\mathcal{C}=-1$. Such spin configuration can be
stablized by pinning the spin orientations on top and bottom layers.
Furthermore, we reveal that the edge states are layer-selective and primarily
locate at the boundaries of the bottom and top layers. In addition, via tuning
the on-site orbital energy which determines the inverted band gap, we find
tunable Chern number from $\mathcal{C}=-1$ to $\mathcal{C}=2$ and then to
$\mathcal{C}=-1$. Our work not only proposes a scheme to realize Chern number
tunable QAHE in antiferromagnets without net spin magnetization, but also
provide a platform for layer-selective dissipationless transport devices.
