  Abstract We theoretically study the realization of quantum anomalous Hall
insulator (QAHI) of composite fermions (CFs) in the twisted bilayer graphene
(TBG) system. We show that the moir\'e pattern in TBG is not only able to
provide a commensurate moir\'e superlattice, but also a tunable effective
periodic potential necessary for the realization, without the need of imposing
an additional superstructure as in the conventional GaAs system. These make the
TBG an ideal platform for realizing the QAHI of CFs. We establish the phase
diagram with respect to tunable experimental parameters based on the Dirac CF
theory. We find that the topological property of the system depends critically
on the orbital magnetic susceptibility of CFs, which is not specified in the
pristine Dirac CF theory. The experimental realization of QAHI of CFs would be
helpful for unveiling the magnetic property of CFs and clarifying the issue.
