In this paper, we deal with channel estimation for Orthogonal Frequency-Division Multiplexing (OFDM) systems. The channels are assumed to be Time-Varying (TV) and approximated by a Basis Expansion Model (BEM). Due to the time-variation, the resulting channel matrix in the frequency domain is no longer diagonal, but can be approximated as banded. Based on this band approximation, we propose novel channel estimators to combat both the noise and the out-of-band interference. Our claims are supported by simulation results, which are obtained based on realistic TV channels with a fairly high Doppler spread.