Optical fiber channel modeling, which is essential in optical transmission system simulations and designs, is usually based on the split-step Fourier method (SSFM), making the simulation quite time-consuming owing to the iteration steps. Here, we train a neural network module termed NNSpan to learn the transfer function of a single fiber (G652 or G655) span with a length of 80 km and successfully emulate long-haul optical transmission systems by cascading multiple NNSpans, which gives remarkable prediction accuracy, even over a transmission distance of 1000 km. Even when trained without erbium-doped fiber amplifier (EDFA) noise, NNSpan performs quite well when emulating the systems affected by EDFA noise. An optical bandpass filter can optionally be added after EDFA, making the simulation more flexible. Comparison with the SSFM shows that NNSpan has a distinct computational advantage, with the computation time reduced by a factor of 12. This method based on NNSpan could be a supplementary option for optical transmission system simulations, thus contributing to system designs as well.