This letter addresses the edge effect on a windowed discrete Fourier transform (WDFT)-based channel estimator for orthogonal frequency division multiplexing (OFDM) systems with virtual carriers in non-sample spaced channels and derives a sufficient condition to reduce the edge effect. Moreover, a modified WDFT-based channel estimator with multi-step linear prediction as an edge effect reduction technique is proposed. Simulation results show that it offers around 5dB signal-to-noise ratio (SNR) gain over the conventional WDFT-based channel estimator at bit error rate (BER) of 10^-3.