A linear analysis of the ExB instability in cyiindrical coordinates in a weakly ionized plasma is studied. It is shown that the qualitative feature of instability is in agreement with Simon's result of slab model. The system is unstable n-hen the sign of the product of the electric field and the density gradient is positive and the applied potential is large enough. It is also shown that the oscillation frequencies of the excited modes fit Saito's experimental results very well in the quantitative feature.