In order to improve the generalization capability of stochastic configuration networks (SCNs), a smooth $L_1$ regularization method for SCNs is proposed. Aiming at the defect of local non-differentiability of the $L_1$ regularization operator, smoothing is carried out in the neighborhood of non-smooth points of the curve. The convex error function of the SCN is constructed on this basis, and an algorithm for incremental calculation of the weights of the SCN is proposed. Furthermore, the global optimization algorithm is proposed based on the alternating direction multiplier method, and the convergence of the algorithm is analyzed theoretically. Compared with the sparsity of $L_1$ regularization and the uniform reduction of parameters by $L_2$ regularization, the proposed method retains all features of the data according to the degree of importance, the parameters are not only kept in a small range, but also have hierarchical distribution, so that the network has better generalization ability. Finally, the feasibility and effectiveness of the proposed method are verified by some numerical simulations.