Blind channel estimation algorithm which is applicable to the time-variant channel under frequency-selective fading is proposed. The condition on the blind channel identifiability using temporally and spatially oversampled data is shown. The proposed algorithm consists of two stages. At the first stage, the channel equalization matrix is estimated by taking account of the time-variant characteristics of the channel. At the second stage, the signals and the channel matrix are alternately estimated by using the finite alphabet property of the transmitted symbols. Periodical return from the second stage to the first makes the blind estimation algorithm feasible for the time-variant channel with fast fading. The simulation results confirm the fast convergence property and the effectiveness of the proposed algorithm in coping with the frequency-selective fading.