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 method, NN-LSA, that leverages convolutional neural networks to generate an initial guess of the frequency, streamwise and spanwise wave numbers, and growth rate of the most unstable mode. Subsequently, the actual values are iteratively calculated based on this initial guess.,The primary advantage of NN-LSA over the traditional e^N method lies in its ability to mitigate the influence of human factors in the stability analysis process, thereby facilitating automatic stability analysis. The application of NN-LSA in boundary layers over flat plates and a sharp cone demonstrates that NN-LSA can obtain characteristics of the most unstable modes consistent with those obtained by traditional global search methods. More importantly, NN-LSA trained by databases of boundary layers over flat plates can be successfully applied in the stability analysis of the boundary layer over a zero-angle-of-attack sharp cone, underscoring its generalization ability.