We have applied two-photon resonant nondegenerate four-wave mixing (NFWM) with a resonant intermediate state to measure the energy levels of the Ba even-parity J=0 and J=2 series. Differing from other experiment techniques, our method is a pure optical technique. Instead of detecting electrons or ions, the signal here is a coherent light. Two-photon resonant NFWM is a Doppler-free spectroscopy when the incident laser beams have narrow bandwidths.