  The effective action of the recently proposed vector Galileon theory is
considered. Using the background field method, we obtain the one-loop
correction to the propagator of the Proca field from vector Galileon
self-interactions. Contrary to the so-called scalar Galileon interactions, the
two-point function of the vector field gets renormalized at the one-loop level,
indicating that there is no non-renormalization theorem in the vector Galileon
theory. Using dimensional regularization, we remove the divergences and obtain
the counterterms of the theory. The finite term is analytically calculated,
which modifies the propagator and the mass term and generates some new terms
also.
