Recent years have witnessed the rapid development of intelligent transportation systems (ITS), which urgently call for highly reliable and effective communication technologies for vehicle-to-vehicle and vehicle-to-infrastructure (V2X) applications. Orthogonal frequency division multiplexing (OFDM) is widely believed to be the most promising candidate among these applications. However, the orthogonality of subcarriers in OFDM can be easily destroyed by the Doppler-induced inter-carrier interference (ICI), which is very common in V2X channels. In this paper, we propose a novel scheme which integrates the ICI self-cancellation technique into the index modulated (IM-) OFDM framework. Via careful designs, the proposed scheme can not only inherit the advantages of IM-OFDM but also suppress the ICI from active subcarriers. Simulations validate that in V2X channels, the proposed scheme significantly outperforms existing IM-OFDM and more importantly shows better performance than the conventional OFDM with ICI self-cancellation without sacrificing the spectral efficiency.