In this paper, the problem of channel estimation in orthogonal frequency-division multiplexing systems over fast time-varying channel is investigated by using a Basis Expansion Model (BEM). Regarding the effects of the Gibbs phenomenon in the BEM, we propose a new method to alleviate it and reduce the modeling error. Theoretical analysis and detail comparison results show that the proposed BEM method can provide improved modeling error compared with other BEMs such as CE-BEM and GCE-BEM. In addition, instead of using the frequency-domain Kronecker delta structure, a new clustered pilot structure is proposed to enhance the estimation performance further. The new clustered pilot structure can effectively reduce the inter-carrier interference especially in the case of high Doppler spreads.