The refinement of the brown dwarf binary fraction may contribute to the understanding of the substellar formation mechanisms. Peculiar brown dwarf spectra or discrepancy between optical and near-infrared spectral type classification of brown dwarfs may indicate unresolved brown dwarf binary systems. We obtained medium-resolution spectra of 22 brown dwarfs of potential binary candidates using X-Shooter at the VLT. We aimed to select brown dwarf binary candidates. We also tested whether BT-Settl 2014 atmospheric models reproduce the physics in the atmospheres of these objects. To find different spectral type spectral binaries, we used spectral indices and we compared the selected candidates to single spectra and composition of two single spectra from libraries, to try to reproduce our X-Shooter spectra. We also created artificial binaries within the same spectral class, and we tried to find them using the same method as for brown dwarf binaries with different spectral types. We compared our spectra to the BT-Settl models 2014. We selected six possible candidates to be combination of L plus T brown dwarfs. All candidates, except one, are better reproduced by a combination of two single brown dwarf spectra than by a single spectrum. The one-sided F-test discarded this object as a binary candidate. We found that we are not able to find the artificial binaries with components of the same spectral type using the same method used for L plus T brown dwarfs. Best matches to models gave a range of effective temperatures between 950 K and 1900 K, a range of gravities between 4.0 and 5.5. Some best matches corresponded to supersolar metallicity.