An instability associated with the magnetosonic wave driven unstable due to coupling with electron and ion drift modes has been considered as a potential source for driving the hydromagnetic turbulence observed in Giacobini-Zinner (G-Z) Cometary plasma. The instability has good growth rate for propagation perpendicular to plasma inhomogeneities and exists for all wave numbers. The wave period for waves propagating perpendicular to the gradients is about a few times ion-gyroperiod and higher values of plasma beta (βe lead to stronger instability.