Spectral detection provides rich spectral–temporal information with wide applications. In our previous work, we proposed a dual-path sub-Hadamard-s snapshot Hadamard transform spectrometer (Sub-s HTS). In order to reduce the complexity of the system and improve its performance, we present a convolution neural network-based method to recover the light intensity distribution from the overlapped dispersive spectra, rather than adding an extra light path to capture it directly. In this paper, we construct a network-based single-path snapshot Hadamard transform spectrometer (net-based HTS). First, we designed a light intensity recovery neural network (LIRNet) with an unmixing module (UM) and an enhanced module (EM) to recover the light intensity from the dispersive image. Then, we used the reconstructed light intensity as the original light intensity to recover high signal-to-noise ratio spectra successfully. Compared with Sub-s HTS, the net-based HTS has a more compact structure and high sensitivity. A large number of simulations and experimental results have demonstrated that the proposed net-based HTS can obtain a better-reconstructed signal-to-noise ratio spectrum than the Sub-s HTS because of its higher light throughput.