Abstract: The e^N method, which has been widely used for predicting boundary-layer transition, necessitates a meticulous search for unstable modes by solving a large number of local boundary-layer stability problems, a process that can be very time-consuming. This paper proposes a novel neural network-based linear stability analysis (NN-LSA) method, that leverages convolutional neural networks to generate an initial guess of the frequency (\omega ), spanwise and streamwise wave numbers ( \beta and \alpha_\rm r ), and growth rate (\sigma_\rm max ) of the most unstable mode. Subsequently, the actual values are iteratively calculated based on this initial guess. The neural network model is trained using a flat plate dataset and the accuracy and computational efficiency of NN-LSA are validated by both flat plate and sharp cone test cases. The results demonstrate that the unstable wave parameters of NN are good agreement with linear stability theory. The LSA component, based on the predicted values provided by NN, can iteratively caculate the most unstable waves. Moreover, the computational time of the NN-LSA method is approximately 20 to 50 times lower than global search method, significantly improving computational efficiency and reducing the influence of human factors in the calculation process. The proposed NN-LSA method enables automated analysis of the linear stability of boundary layer flows and shows promising potential for practical applications.