Shear wave splitting parameters obtained along a linear array of 23 stations deployed in western Tibet during a two-year period from 2011 to 2013 demonstrate strong and systematic azimuthal variations with a 90-degree periodicity, suggesting the existence of double-layer anisotropy with a horizontal axis of symmetry. The predominant fast orientations are mostly E-W for events from the east and southeast, and NE-SW or N-S for events from the northwestern quadrant. Under the assumption of a two-layer anisotropic structure, we grid-search for the two pairs of parameters that characterize the complex anisotropy. The resulting fast orientation for the lower layer is mostly N-S, which is consistent with the direction of mantle flow caused by the subduction of the Indian continent beneath Tibet. For the upper layer, the fast orientation is NE-SW, which is significantly different from the strike of dominant surface structures, and can be explained by lower crustal flow in western Tibet. This interpretation is supported by the NE-SW orientation and significant strength (with splitting times as large as 1.3 s) of crustal anisotropy revealed using the sinusoidal moveout of the P-to-S converted phases from the Moho. To our knowledge, this is the first time when upper layer anisotropy revealed from SWS analysis is reliably constrained in the crust using independently determined crustal anisotropy measured by the P-to-S converted phase from the Moho. The observations provide additional evidence for the existence of a subducted Indian slab that is undeformed and is decoupled from the significantly shortened crust, extending to the northern margin of the Qiangtang block.