Electrohydrodynamic (EHD) flows of dielectric liquid are ubiquitous in engineering applications such as heat transfer, pumping and mixing. Present study describes the numerical simulation of EHD flow instability in the annular gap between two concentric circular cylinders with unipolar and bipolar charge injection. The Nernst-Planck equations governing the charge density transport, the Poisson equation for the electric potential and the Navier-Stokes equations for the fluid flow are solved numerically using the finite volume method. The developed code was validated by comparing values of T C, the critical parameter for the onset of electro-convection, with those given by a linear instability analysis. We have found that the outer-injection case is more stable than the inner injection, but it becomes more unstable with increase of the inner cylinder size (r i), whereas the trend is opposite in the inner-injection case. The wave number characterizing the vortical flow increases with r i in agreement wim the linear analysis. We identify in a parameter space the stable hydrostatic state and the electro-convection state. The electro-convection state is again divided into three regimes; stationary, oscillatory and chaotic. For the bipolar injection case we observed travelling-wave-type vortical flows at a certain parameter set. The wave number of the travelling-wave vortical flow shows regular fluctuations for certain parameter set, which was confirmed from the beat like variations in the fluid velocity.