  New Dirac points appear when periodic potentials are applied to graphene, and
there are many interesting effects near these new Dirac points. Here we
investigate the $\textit{Zitterbewegung}$ effect of fermions described by a
Gaussian wave packet in graphene superlattice near new Dirac points. The
$\textit{Zitterbewegung}$ near different Dirac points has similar
characteristics, while Fermions near new Dirac points have different group
velocities in both $x$- and $y$-direction, which causes the different
properties of the $\textit{Zitterbewegung}$ near new Dirac points. We also
investigate the $\textit{Zitterbewegung}$ effect influenced by all Dirac
points, and get the evolution with changing potential. Our intensive results
suggest that graphene superlattice may provide an appropriate system to study
$\textit{Zitterbewegung}$ effect near new Dirac points experimentally.
