  The interlayer antiferromagnetic coupling hinders the observation of quantum
anomalous Hall effect in magnetic topological insulator MnBi$_2$Te$_4$. We
demonstrate that interlayer \textit{ferromagnetism} can be established by
utilizing the \textit{p}-doping method in MnBi$_2$Te$_4$ multilayers. In two
septuple-layers system, the interlayer ferromagnetic coupling appears by doping
nonmagnetic elements (e.g., N, P, As, Na, Mg, K, and Ca), due to the
redistribution of orbital occupations of Mn. We further find that Mg and Ca
elements are the most suitable candidates because of their low formation
energy. Although, the \textit{p}-doped two septuple layers exhibit
topologically trivial band structure, the increase of layer thickness to three
(four) septuple layers with Ca (Mg) dopants leads to the formation of the
quantum anomalous Hall effect. Our proposed \textit{p}-doping strategy not only
makes MnBi$_2$Te$_4$ become an ideal platform to realize the high-temperature
quantum anomalous Hall effect without external magnetic field, but also can
compensate the electrons from the intrinsic \textit{n}-type defects in
MnBi$_2$Te$_4$.
