In this paper, we introduce the notion of I2-convergence in T0 spaces, and study the fundamental properties of I2-topology which is determined by I2-convergence according to the standard topological approach. Then, we give a sufficient condition for I2-convergence to be topological. Finally, we introduce a special class of T0 spaces, called IDC-spaces, and then present a sufficient and necessary condition for I2-convergence to be topological in IDC-spaces.