Quantum anomalous Hall (QAH) effect is a quantum Hall effect that occurs without the need of exteal magnetic field.A system composed of multiple parallel QAH layers is an effective high Che number QAH insulator and the key to the applications of the dissipationless chiral edge channels in low energy consumption electronics.Such a QAH multilayer can also be engineered into other exotic topological phases such as a magnetic Weyl semimetal with only one pair of Weyl points.This work reports the first experimental realization of QAH multilayers in the superlattices composed of magnetically doped (Bi,Sb)2 Te3 topological insulator and CdSe normal insulator layers grown by molecular beam epitaxy.The obtained multilayer samples show quantized Hall resistance h/Ne2,where h is Plancks constant,e is the elementary charge and N is the number of the magnetic topological insulator layers,resembling a high Che number QAH insulator.The QAH multilayers provide an excellent platform to study various topological states of matter.