Linear polarization due to scattering processes can be used as a probe of the existence of atmospheric condensates in ultracool dwarfs. Models predict that the observed linear polarization increases with the degree of oblateness, which is inverse to the surface gravity.We aimed to measure optical linear polarization from a sample of six young brown dwarfs, with spectral types between M6 to L2, and cataloged previously as objects with low gravity using spectroscopy. These targets are believed to have dusty atmospheres as a consequence of their low gravity, therefore linearly polarized light is expected from these objects.Linear polarimetric data were collected in I and R-band using CAFOS at the 2.2m telescope in Calar Alto Observatory.We obtained results of linear polarization in the I-band compatible with non polarization for all the objects, and similar results for the polarization degree in the R-band for all objects with the exception of 2M0422. For this object we find a linear polarization degree of 0.81+-0.18%. 2M0422 is 10 deg to the south of the Taurus star-forming region, thus, we suspect that its polarization is caused by the dust in the cloud in which 2M0422 might be embedded.