  We calculate the gluon dissociation cross-section in an anisotropic quark
gluon plasma expected to be formed due relativistic nucleus-nucleus collisions.
The initial rapid longitudinal expansion of the system leads to momentum space
anisotropy due which the observables are affected in such a system. We show
that the thermally weighted cross-section of gluon dissociation undergoes
modification in anisotropic plasma leading to a decreased probability of
$J/\psi$ suppression both for RHIC and LHC energies. The dependence of the
cross section as well as the survival probability on the direction of
propagation of the charmonium with respect to the anisotropy axis are
presented. The sensitivity of the survival probability on the initial
conditions have also been demonstrated.
