The min-sum (MS) decoding for low-density parity-check codes, though less complex than the sum–product algorithm, suffers from worse error-correcting performance. For enhancement, neural MS decoders leveraging deep learning have recently been introduced, but how to train them has not been sufficiently discussed. In this paper, we propose a novel dataset construction method and also propose systematic learning strategies by finding a good combination of dataset composition, loss functions, weight sharing, weight assignment, and weight update method. Simulations demonstrate that the proposed method achieves better error-correcting performance than other works, especially in the error floor region, within a limited number of iterations.