Vehicle-to-Vehicle and Vehicle-to-Infrastructure (V2X) communication brings about stringent demand for robust and efficient communication techniques under sever Doppler effect and frequency-selective channel environments. Index Modulated Orthogonal Frequency Division Multiplexing with Interleaved grouping (IIM-OFDM), which utilizes the indices of active subcarriers in frequency domain interleaved subcarrier groups to carry information, is considered as a competitive candidate for its robustness against both Inter-Carrier Interference (ICI) and channel correlation. In this paper, we propose a novel revision of IIM-OFDM designed for V2X, namely Quadrature Index Modulated OFDM with Interleaved grouping (IQIM-OFDM), which performs index modulation independently for the inphase and quadrature components of the constellation symbols. Thanks to the increased index bits, IQIM-OFDM can work at smaller subcarrier group and constellation sizes compared with IIM-OFDM at the same data rate, and therefore boosts the performance under V2X channels. Monte Carlo simulations under measured V2X channels are conducted to verify the superiority of the proposed scheme against both IIM-OFDM and classical OFDM schemes.