Orthogonal frequency division multiplexing (OFDM) channel estimation is the key technique used in broadband wireless networks. The Doppler frequency caused by fast mobility environments will cause inter-carrier interference (ICI) and degrade the performance of OFDM systems. Due to the severe ICI, channel estimation becomes a difficult task in higher mobility scenarios. Our aim is to propose a pilot-aided channel estimation method that is robust to high Doppler frequency with low computational complexity and pilot overheads. In this paper, the time duration of each estimate covers multiple consecutive OFDM symbols, named a “window”. A close-form of polynomial channel modeling is derived. The proposed method is initialized to the least squares (LS) estimates of the channels corresponding to the time interval of the pilot symbols within the window. Then, the channel interpolation is performed in the entire window. The results of computer simulations and computation complexity evaluations show that the proposed technique is robust to high Doppler frequency with low computation complexity and low pilot overheads. Compared with the state-of-the-art method and some conventional methods, the new technique proposed here has much lower computational complexity while offering comparable performance.