In the field of time series data prediction, designing an appropriate neural network requires considering issues such as feature selection and the specific architecture of the network based on the dataset. This demands engineers to have a solid understanding of neural network theory, posing a high entry barrier. Aiming to solve this problem, this paper proposes a two-stage self-adaptive neural network design method called AutoDesign-Net. This method can automatically perform feature selection and construct neural networks without requiring manual intervention in the design details, thus lowering the threshold for engineers. In the first stage, AutoDesign-Net uses an optimized genetic algorithm to automatically select features and determine the optimal neural network architecture suited for the prediction task of the given dataset. In the second stage, based on the network structure obtained in the first stage, the method further optimizes the neural network weights to enhance prediction performance. With this approach, the most suitable feature selection strategy and neural network can be identified for any given dataset, leading to satisfactory prediction results. AutoDesign-Net has been validated on open datasets and demonstrates outstanding performance compared to several existing methods.