Surrogate can greatly reduce the computing cost of full-wave electromagnetic simulation software in antenna design, and neural networks as a kind of surrogate have become very popular in recent years, among which the Convolutional Neural Network (CNN) is a very hot topic due to its better feature extraction and generalization capability. In this paper, Broad Learning System (BLS) is introduced to address the problems that CNN may fall into with local optimization and overfitting when dealing with antenna data. It provides a learning method to increase nodes in width for regression prediction, which has good generalization ability. Specifically, in antenna design, feature extraction is first applied using the convolution and pooling of CNN. The original dataset is combined with the extracted feature data to realize data augmentation, and then the BLS is used for regression training. Compared with the traditional deep CNN, this model uses lightweight convolutional layers, which is promising in solving the problem of the network falling into local optimum or overfitting. The simulation results show that the accuracy reaches 93.91% and 92.34% respectively on the Abalone benchmark and antenna data, proving the effectiveness of the proposed model in this paper.