  Quasi-parton distribution functions have received a lot of attentions in both
perturbative QCD and lattice QCD communities in recent years because they not
only carry good information on the parton distribution functions, but also
could be evaluated by lattice QCD simulations. However, unlike the parton
distribution functions, the quasi-parton distribution functions have
perturbative ultraviolet power divergences because they are not defined by
twist-2 operators. In this paper, we identify all sources of ultraviolet
divergences for the quasi-parton distribution functions in coordinate-space,
and demonstrate that power divergences, as well as all logarithmic divergences
can be renormalized multiplicatively to all orders in QCD perturbation theory.
