  A van der Waals heterostructure combined with intrinsic magnetism and
topological orders have recently paved attractive avenues to realize quantum
anomalous Hall effects. In this work, using first-principles calculations and
effective model analysis, we propose that the robust quantum anomalous Hall
states with sizable band gaps emerge in the van der Waals heterostructure of
germanene/Cr$_2$Ge$_2$Te$_6$. This heterostructure possesses high thermodynamic
stability, thus facilitating its experimental fabrication. Furthermore, we
uncover that the proximity effect enhances the coupling between the germanene
and Cr$_2$Ge$_2$Te$_6$ layers, inducing the nontrivial band gaps in a wide
range from 29 meV to 72 meV. The chiral edge states inside the band gap,
leading to Hall conductance quantized to $-e^2/h$, are clearly visible. This
findings provide an ideal candidate to detect the quantum anomalous Hall states
and realize further applications to nontrivial quantum transport at a high
temperature.
