Next generation large sky surveys will observe up to billions of galaxies for which basic structural parameters are needed to study their evolution. This is a challenging task that, for ground-based observations, is complicated by the seeing limited point-spread-function (PSF). To perform fast and accurate analysis of galaxy surface brightness, we have developed a family of supervised Convolutional Neural Network (CNN) tools to derive Sersic profile parameters of galaxies. In this work, we present the first two Galaxy Light profile convolutional neural Networks (GaLNets) of this family. A first one, trained using galaxy images only (GaLNet-1), and a second one, trained with both galaxy images and the local PSF (GaLNet-2). We have compared the results from the two CNNs with structural parameters (namely the total magnitude, the effective radius, Sersic index etc.) derived on set of galaxies from the Kilo-Degree Survey (KiDS) by 2DPHOT, as a representative of "standard" PSFconvolved Sersic fitting tools. The comparison shows that, provided a suitable prior distribution is adopted, GaLNet-2 can reach an accuracy as high as 2DPHOT, while GaLNet-1 performs slightly worse because it misses the information on the local PSF. In terms of computational speed, both GaLNets are more than three orders of magnitude faster than standard methods. This first application of CNN to ground-based galaxy surface photometry shows that CNNs are promising tools to perform parametric analyses of very large samples of galaxy light profiles, as expected from surveys like Vera Rubin/LSST, Euclid and the Chinese Space Station Telescope.