  We give a combinatorial classification of torus equivariant vector bundles on
a (normal) projective T-variety of complexity-one. This extends the
classification of equivariant line bundles on complexity-one T-varieties by
Petersen-S\"uss on one hand, and Klyachko's classification of equivariant
vector bundles on toric varieties on the other hand. A main ingredient in our
classification is the classification of torus equivariant vector bundles on
toric schemes over a DVR in terms of piecewise affine maps to the (extended)
Bruhat-Tits building of the general linear group.
