The purpose of this paper is to investigate the spectra of the Dirac operator H = H-o + V - -icalpha . del + betamc(2) + V. The local compactness of H is shown under some assumption on V. This method enables us to prove that if \V(x) - abeta\ --> 0 as \x\ --> infinity, then sigma(ess)(H) = (-infinity, -mc(2) - a] boolean OR [mc(2) + a, infinity) and to give a significant sufficient condition that H+ or H- has a purely discrete spectrum.