The radial and transverse receiver functions obtained at several stations located on the Songpan-Ganze terrane (Tibetan plateau) are characterized by strong P to S conversions in the first 4 s after the direct P wave. We show that the amplitude variations of these phases with back-azimuth can be well explained by a simple model with one or two anisotropic layers. The anisotropy we obtained is quite strong (about 15%) and might be related to the presence of highly deformed flyschs and schists in the first 25 km of the crust. This study shows that anisotropy in the crust could be locally high and has to be taken into account when analyzing teleseismic data.