Trajectory prediction is very important to navigation safety, marine traffic control and surface vessels search. In order to improve the accuracy of vessel trajectory prediciton and according to the multi-dimensional characteristics of vessel trajectory features, a new model named parallel LSTM-FCN(PLSTM-FCN) is proposed. The model can exact features and trend from multi-dimensional vessel trajectory, because of combining with the LSTM which has advanced to predict time series trend and the fully convolutional networks(FCN) which is adept in exacting detail features of time series. Simultaneously, the training efficiency of the PLSTM-FCN which has more parameters is the same as the LSTM-FCN, because of the concurrent design. In order to improve the learning efficiency, a preprocessing method based on the dynamic time warping algorithm and the Laida criterion is proposed. The simulation experiment is carried out based on the data of automatic identification systems(AIS). Experimental results show that the PLSTM-FCN is more accurate than the typical RNN in vessel trajectory prediction.