In this paper, we propose a new regular-shaped geometry-based stochastic model (RS-GBSM) for non-isotropic scattering wideband multiple-input multiple-output vehicle-to-vehicle (V2V) Ricean fading channels. By correcting the unrealistic assumption widely used in current RS-GBSMs, the proposed model can more practically study the impact of the vehicular traffic density on channel statistics for different time delays. From the proposed model, we derive the Doppler power spectral density (PSD) and find that highly dynamic Doppler spectrum appears for V2V channels. Excellent agreement is achieved between the derived Doppler PSD and measured data, demonstrating the utility of the proposed model. To combat the intercarrier interference (ICI) caused by highly dynamic Doppler spectrum in real orthogonal frequency division multiplexing based V2V systems, this paper proposes a new type of ICI cancellation scheme, named as precoding based cancellation (PBC) scheme. The proposed scheme can be easily implemented into real V2V systems with the same ICI mitigation performance as the current best ICI cancellation scheme that has high complexity. To further improve the performance of the proposed PBC scheme, a new phase rotation aided (PRA) method, namely constant PRA (CPRA) method, is proposed. Compared with the existing PRA method, the CPRA method has better performance and much less implementation complexity. Therefore, the proposed PBC scheme with the CPRA method is the best ICI cancellation scheme for real V2V systems.