We present a nonperturbative variational method for calculating the glueball mass with an explicit color vector potential present. Using a two-body relativistic wave equation for bound states in quantum chromodynamics we examine the gluonium state including a Darwin-type color vector potential with a QCD-motivated scalar potential. Our equations are solvable variationally for the energy, in the Coulomb gauge, with spin interactions. We find that for theS-states, where the vector potential contributions are the largest, the effect on the bound-state energy is not negligible. In particular the ground state 0++ glueball has a mass of 1215 MeV.