Abstract: ‍ ‍Broad learning system （BLS） is a new kind of discriminative learning method proposed in recent years. It has the characteristics of simple structure and fast training， and has been widely used in various regression and classification problems. However， the standard BLS is derived under the Minimum Mean Square Error （MMSE） criterion， which is very sensitive to the existence of outliers， which undoubtedly reduces the accuracy of the system. In order to improve the robustness of BLS， some scholars have proposed BLS with maximum correntropy criterion （MCC） （C-BLS）. Compared with the minimum mean square error criterion， the maximum correntropy criterion contains more high-order error information， so C-BLS has good robustness to outliers. However， considering that the default kernel function in correntropy is fixed as Gaussian kernel， this is not applicable in the vast majority of cases. In this paper， the generalized correntropy with generalized Gaussian density （GGD） function as the kernel function is introduced， and the generalized maximum correntropy criterion （GMCC） is applied to BLS， and a new robust algorithm （GC-BLS） is proposed. GC-BLS can be regarded as a special case of GC-BLS. When appropriate parameters are selected， GC-BLS will degenerate to C-BLS， which makes the new algorithm at least obtain the same performance as C-BLS algorithm. In the experiment， the root mean square error is used as the standard to test the new algorithm on regression data sets and time series data sets. In most cases， GC-BLS can achieve smaller root mean square error than other algorithms. Experiments show that the algorithm is very stable. Simulation results validate the theoretical expectations and demonstrate the performance of the new algorithm.