Summary: Levinson's theorem is generalized to relativistic scalar particles satisfying the Klein-Gordon equation with a spherically symmetric potential \(V(r)\), which is the fourth component of a vector field, and shown to be \[ N_l=n_l^{(+)}-n_l^{(-)}=(1/\pi)[\delta_l(M)+ \alpha_1]-(1/\pi)[\delta_l(-M)+\alpha_2], \] where \(N_l\) denotes the difference of the numbers of the particle bound states and the antiparticle ones with a definite angular momentum \(l\), \(\delta_l(E)\) is the phase shift, and \(\alpha_1\) and \(\alpha_2\) are constants reflecting the critical cases where bound states or half bound states occur at \(E=\pm M\).