  Recently, quantum oscillation of the resistance in insulating monolayer
WTe$_2$ was reported. An explanation in terms of gap modulation in the
hybridized Landau levels of an excitonic insulator was also proposed by one of
us. However, the previous picture of gap modulation in the Landau levels
spectrum was built on a pair of well nested electron and hole Fermi surfaces,
while the monolayer WTe$_2$ has one hole and two electron Fermi pockets with
relative anisotropy. Here we demonstrate that for system like monolayer
WTe$_2$, the excitonic insulating state arising from the coupled one hole and
two electron pockets possesses a finite region in interaction parameter space
that shows gap modulation in a magnetic field. In this region, the thermally
activated conductivity displays the $1/B$ periodic oscillation and it can
further develop into discrete peaks at low temperature, in agreement with the
experimental observation. We show that the relative anisotropy of the bands is
a key parameter and the qunatum oscillations decrease rapidly if the anisotropy
increases further than the realistic value for monolayer WTe$_2$.
