When trying to estimate time-varying multipath channels by applying a basis expansion model (BEM) in orthogonal frequency division multiplexing (OFDM) systems, pilot clusters are contaminated by inter-carrier interference (ICI). The pilot cluster ICI (PC-ICI) degrades the estimation accuracy of BEM coefficients, which degrades system performance. In this paper, a PC-ICI suppression scheme is proposed, in which two coded symbols defined as weighted sums of data symbols are inserted on both sides of each pilot cluster. Under the assumption that the channel has Flat Doppler spectrum, the optimized weight coefficients are obtained by an alternating iterative optimization algorithm, so that the sum of the PC-ICI generated by the encoded symbols and the data symbols is minimized. By approximating the optimized weight coefficients, they are independent of the channel tap power. Furthermore, it is verified that the proposed scheme is robust to the estimation error of the normalized Doppler frequency offset and can be applied to channels with other types of Doppler spectra. Numerical simulation results show that, compared with the conventional schemes, the proposed scheme achieves significant improvements in the performance of PC-ICI suppression, channel estimation and system bit-error-ratio (BER).