In this paper, a low complexity iterative intercarrier interference (ICI) cancellation and equalization technique is proposed for use in OFDM systems over doubly selective channels. In the iterative parallel interference cancellation/minimum mean square error (PIC/MMSE) detector has a high complexity and a restriction on the structure which can not remove the ICI in the initial stage. Therefore, an error propagation occurs due to the ICI regenerated by the incorrect output of soft-input soft-output (SISO) decoder. In order to reduce the error propagation, an MMSE detector based on the successive interference cancellation (SIC) is used in the initial stage. The low complexity MMSE detector is also derived to minimize the error propagation by quantifying the decision error before SISO decoding. In the first iteration, simulation results show that the proposed scheme outperforms the conventional PIC/MMSE scheme by about 3 dB at bit error rate $({\rm BER})=1\times 10^{-3}$ while maintaining the equivalent computational complexity. In the subsequent iteration, it is possible to cancel the ICI out in the received signals by the aid of soft log-likelihood ratio (LLR) fed from the SISO decoder. Converting the LLR to the decision error probability, the error covariance matrix is obtained more accurately. As a result, the error propagation can be effectively reduced by dealing with only the dominant components, when considering decision errors. Finally, simulation results show that the proposed scheme outperforms the conventional PIC/MMSE scheme.