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The two-dimensional (2D) electro-convection (EC) flow of dielectric liquids between two concentric cylindrical electrodes driven by unipolar injection of ions is investigated numerically. The finite volume method is used to resolve the spatiotemporal distributions of the flow field, electric field, and charge density. The flow transition routes from steady laminar to chaotic flow states are studied in various scenarios where the mobility parameter M of the dielectric liquids varies from 5 to 200. The dynamic characteristics and bifurcation routes of the EC flow depend on the electric Rayleigh number T, a ratio of the electric force to viscous force, and the mobility parameter M. For increasing T, three different transition routes from a convective steady-state to chaos via different intermediate states are observed. The flow states have been quantified by the power spectral density distribution and phase space trajectory of the velocity. The fractal dimensions and Lyapunov exponents are calculated to identify the chaotic flow. The increase in the mobility parameter M leads to a shorter and more direct route with fewer intermediate states when bifurcating to chaos. In addition, the power scale of charge transport that is defined by the electric Nusselt number Ne and T is discussed when the EC flow develops into electro-turbulence.