In this paper, we propose low complexity channel parameter tracking methods for adaptive OFDM MMSE channel estimation. Even though the MMSE estimation is one of the most accurate channel estimation methods, it requires several channel information including Doppler frequency, RMS (root mean squared) delay spread, and SNR. To implement the MMSE estimation, tracking of such parameters should be preceded. We propose methods to track the above 3 channel parameters. As for Doppler frequency estimation, we propose an extremum method with a parabolic model, which is a key contribution of this paper. We also analyze the computational complexity of the proposed algorithms. Simulations show that the proposed tracking algorithm tracks the parameters well, and performs better than the conventional fixed-parameter algorithm in terms of BER performance. The BER performance of the adaptive MMSE estimation is better than that of a fixed-parameter (robust) MMSE estimator by about 5 dB.