Given that the existing design of experiments methods are unable to perform the efficient design of experiments for complex systems, this paper proposes a design of experiments method based on the variational auto-encoder. First, experimental historical data are used to train the variational auto-encoder to encode the complex experimental sample space into a relatively simple latent variable space. Then, samples are obtained from the latent variable space. Finally, new experimental samples are generated by the decoder through restoration, and the design of experiments is achieved. The performance of the proposed method in fitting the hit model of the straight-running torpedo is compared with those of several benchmark design of experiments methods. It is shown that with the same number of samples, the proposed method can optimize the design of experiments and improve the efficiency of the experiments.