Transferable local pseudopotentials (LPPs) are essential for fast quantum simulations of materials. However, various types of LPPs suffer from low transferability, especially since they do not consider the norm-conserving condition. Here we propose a novel approach based on a deep neural network to produce transferable LPPs. We introduced a generalized Kerker method expressed with the deep neural network to represent the norm-conserving pseudo-wavefunctions. Its unique feature is that all necessary conditions of pseudopotentials can be explicitly considered in terms of a loss function. Then, it can be minimized using the back-propagation technique just with single point all-electron atom data. To assess the transferability and accuracy of the neural network-based LPPs (NNLPs), we carried out density functional theory calculations for the s- and p-block elements of the second to the fourth periods. The NNLPs outperformed other types of LPPs in both atomic and bulk calculations for most elements. In particular, they showed good transferability by predicting various properties of bulk systems including binary alloys with higher accuracy than LPPs tailored to bulk data.