Very Short-term prediction of ship motion is critically important in many scenarios such as carrier aircraft landings and marine engineering operations. This paper introduces the newly developed functional deep learning model, named as Deep Operator Networks neural network(DeepOnet) to predict very short-term ship motion in waves. It takes wave height as input and predicts ship motion as output, employing a cause-to-effect prediction approach. The modeling data for this study is derived from publicly available experimental data at the Iowa Institute of Hydraulic Research. Initially, the tuning of the hyperparameters within the neural network system was conducted to identify the optimal parameter combination. Subsequently, the DeepOnet model for wave height and multi-degree-of-freedom motion was established, and the impact of increasing time steps on prediction accuracy was analyzed. Lastly, a comparative analysis was performed between the DeepOnet model and the classical time series model, LSTM. It was observed that the DeepOnet model exhibited a tenfold improvement in accuracy for roll and heave motions. Furthermore, as the forecast duration increased, the advantage of the DeepOnet model showed a trend of strengthening. As a functional prediction model, DeepOnet offers a novel and promising tool for very short-term ship motion prediction.