The microstructure and current transport behavior in the thermally nitrided silicon oxide (SiOxNy) thin films have been studied and a new model is proposed to explain the current transport behavior of the films. In particular, the model includes the case in which the external applied high field rises up to the value just before the occurance of intrinsic breakdown. The theoretical result of the new model agrees well with the experiment. Finally, the significant current enhancement and trapping ledge phenomenon in the I-V characteristics of the films have been explained satisfactorily using this new model, and the influences of the external applied field and the electron trap on the current transport behavior in the films are also discussed.