Abstract: To solve the problems of Doppler sensitivity and low spectral efficiency of the coherent and non-coherent communication commonly used in orthogonal frequency division multiplexing (OFDM) underwater acoustic communication, a semi-coherent communication technique with M-ary amplitude shift keying is proposed, in which, all the frequencies in the OFDM symbolic time-frequency frame structure are modulated with M-ary amplitude shift keying and the semi-coherent channel estimation is accomplished with the signal amplitude information. By optimizing the nonlinear process of semi-coherent channel estimation with two deep learning algorithms, the spectral efficiency is improved compared to the non-coherent communication and the robustness is improved; meanwhile, the bit error rate and system complexity are reduced compared to the coherent communication at a certain signal to noise ratio. Moreover, the meta-learning-based algorithm is used to reduce the dependence of the deep learning algorithm on the training data. Finally, the simulation of OFDM semi-coherent underwater acoustic communication system is completed by using the actual channel data obtained from sea trial, and the results verify the advantages of the proposed method over non-coherent and coherent communication in terms of spectral efficiency and system bit error rate. And, the meta-learning-based algorithm can still obtain better performance when the channel length changes.