Comparing with the terrestrial wireless channel, underwater acoustic (UA) channel is severely affected by strong impulsive noise, time variation and frequency variation. Except for channel estimation and channel equalization, symbol detection (SD) is also a significant part in the procedure of signal processing. In this paper, we propose a multilayer perceptron (MLP) neural network-based algorithm to manage the symbol detection task in UA communication. The neural network can learn more characters of UA channel and perform the task of signal processing effectively. From the view of MLP, the problem of constellation demodulation can be considered as an estimation of output symbols' probability. The cross entropy and recitified linear unit (ReLU) are used as loss function and activation function respectively. The traditional least-squares (LS) estimation and blanking combined with MLP-based symbol detection can have better performance on symbol-error-rate (SER). The proposed model is evaluated through numerical simulations with different parameters and real data collected during a UA communication experiment in December 2015 in the estuary of the Swan River, Western Australia. The results show that the proposed algorithm has a better performance than the existing method.