This paper considers the channel estimation method in the case of a high mobility communication in orthogonal frequency-division multiplexing (OFDM) systems. In this paper, several successive OFDM symbols experienced channel are treated as a window. The polynomial approximation of the channel parameters in the time domain is considered. We show that the low order polynomials are good enough to model the channel within a window. Hence the interpolation performing over a whole window profits pilot reduction. Moreover, the method has an advantage of computational complexity because of the low order polynomial approximation and without the requirement of inter-carrier interference mitigation. The method is derived with the least-square approach for polynomial interpolation of arbitrary order. Simulation results show that the proposed method is robust to high Doppler frequency and enhancing the transmission efficiency.