This paper proposes a sparsity method for network structure of broad learning system (BLS) based on lasso and elastic net. The L-norm in the standard BLS objective function is replaced by the lasso and the elastic net respectively. These two regularization techniques are used to constrain the output weight of each network node, so as to measure the impact of each node's output weight on the prediction. In this way, the redundant nodes are eliminated and the sparsity of network structure is improved. Through the experiments on some regression datasets, it can be seen that the proposed method can simplify the network structure without losing the prediction accuracy.