  The TeV $\gamma$-ray halo around the Geminga pulsar is an important indicator
of cosmic-ray (CR) propagation in the local zone of the Galaxy as it reveals
the spatial distribution of the electrons and positrons escaping from the
pulsar. Considering the intricate magnetic field in the interstellar medium
(ISM), it is proposed that superdiffusion model could be more realistic to
describe the CR propagation than the commonly used normal diffusion model. In
this work, we test the superdiffusion model in the ISM around the Geminga
pulsar by fitting to the surface brightness profile of the Geminga halo
measured by HAWC. Our results show that the chi-square statistic monotonously
increases as $\alpha$ decreases from 2 to 1, where $\alpha$ is the
characteristic index of superdiffusion describing the degree of fractality of
the ISM and $\alpha=2$ corresponds to the normal diffusion model. We find that
model with $\alpha<1.32$ (or $<1.4$, depending on the data used in fit) is
disfavored at 95\% confidence level. Superdiffusion model with $\alpha$ close
to 2 can well explain the morphology of the Geminga halo, while it predicts
much higher positron flux on the Earth than the normal diffusion model. This
has important implication for the interpretation of the CR positron excess.
