In order to understand the phenomena in the solar chromosphere and their complex physical processes, it is required to quantitatively diagnose the physical properties of chromospheric plasmas. Recently, a multilayer spectral inversion (MLSI) model has been proposed to infer the physical parameters of plasmas in the solar chromosphere. The inversion solves a three-layer radiative transfer model using the H alpha and Ca II 8542 Å line profiles taken by the Fast Imaging Solar Spectrograph (FISS). The model successfully provides the physical plasma parameters. However, it is computationally expensive to apply the MLSI to a huge number of line profiles. For example, the calculating time is an hour to several hours for a scanned raster observation. To reduce the cost of calculating the physical parameters, we apply a deep learning method (Deep Neural Networks) to the inversion code. Our deep learning model successfully reproduces physical parameter maps of a scanned raster per second. In this talk, I will present a concept of our fast spectral inversion model based on deep learning techniques, and discuss the performance of the model and our future plans.