In order to estimate fast time-varying channels exactly, the Inter-Carrier Interference (ICI) caused by time-varying fading channels in Orthogonal Frequency Division Multiplexing (OFDM) systems is analyzed based on the Basis Expansion Model (BEM). A channel estimation and ICI cancellation algorithm with low complexity is proposed. A special pilot sequence is designed to minimize the cost of computing the channel state information in the proposed algorithm. Based on the property of channel frequency impulse matrix, the ICI can be canceled iteratively in frequency domain. The complexity of the algorithm is analyzed theoretically. Through simulation, the algorithm is shown to be effective in estimating channel state information and in cancelling ICI.