A Doppler estimation system using a maximum likelihood criterion is presented in the context of underwater acoustic communications between moving transmitter/receiver. We simulate the method for the estimation of the Doppler effect induced by an underwater acoustic channel (UWA) using Zero Padded-Orthogonal Frequency Division Multiplexing (ZP-OFDM). Among the wide range of physical processes that impact OFDM communications through the underwater environment, Doppler effect is an important cause of loss of orthogonality and must be compensated before discrete Fourier transform based demodulation can be performed. The proposed approach is based on the perfect knowledge of the emitted signal during one block and rely on the assumptions of a small variation of the Doppler effect induced by the canal between two ZP-OFDM blocks and, above all, during one block.