Abstract: As well known Fano resonance arises from interference between a localized state and a continuum state. Using standard Floquet theory and scattering matrix method, we study theoretically the massive Dirac particle transmission over a quantum barrier with an oscillating field. It is found that the massive relativistic particles can arise not only normal Fano resonance in the transmission due to interference between a localized state (bound state) and the continuum state, but also anomalous Fano resonance in the transmission due to interference between a delocalized state (extended state) and the continuum state. The dependence of line shapes on driving parameters for such two kinds of Fano resonances are quite different. For normal Fano resonance the asymmetry parameter is approximately proportional to a power law of amplitude of oscillating field, while for the anomalous Fano resonance the asymmetry parameters change slightly with different oscillation amplitudes. In actual experiment anomalous Fano resonance can be identified by observing asymmetry parameter, and it can be implemented in experiment.