  The Crab pulsar and its nebula are very luminous and variable. Since 1982,
random fluctuations of the dispersion measure (DM) have been recorded. Also in
2011, Fermi-LAT telescope detected $\gamma$-ray flux variation of the Crab
nebula. No correlation between these phenomena have considered although their
fluctuating patterns look similar. We propose a model which connects the DM and
the Crab nebula $\gamma$-ray flux fluctuation, motivated by recently reported
correlation between the braking index and the DM variability. Considering
electrons within the inner shock region of the nebula produced in breaking
index change events, we can explain both the DM enhancement and the
$\gamma$-ray flare in a simple way.
