A meta-learning (ML) based time-varying channel estimation method with inter-carrier interference (ICI) cancellation is proposed for the high-speed mobile OFDM systems. To reduce the effect of the ICI caused by the Doppler shift on the accuracy of channel estimation, a improved transformation matrix is given to transform the transmitted signal with the comb-type pilot in the frequency domain into the one with the block-type pilot in the time domain, which can reduce the interference of the neighboring data symbols to the pilots. Since the ML network has ability to quickly adapt to the new channel scenario, it is employed to estimate the time-varying channel only by the received ICI-free pilots. To improve the practicability of the estimation model, the training target of the network is set as the channel estimation with high accuracy rather than the ideal channel state information. Simulation results show that the proposed method has high estimation accuracy and low computational complexity, and it is robust to the fast time-varying channel in the high-speed mobile scenarios.