  In this paper we complete formulae for the elastic cross section of general
vector dark matter with nucleon in the direct detection at the leading order of
the strong coupling constant, assuming that the dark matter is composed of
vector particles. As an application of our formulae, the direct detection of
the first Kaluza-Klein photon in the minimal universal extra dimension model is
discussed. It is found that the cross section is larger than those in the
previous works by up to a factor of ten.
