The change of the polarization state of a HeNe laser is observed when the cavity length is increasing, it is found that one of its polarized state is always bright, and the other polarized state is always dark. Only in process of mode conversion, the latter has opportunity to oscillate but extinguish immediately, and at the same time their power changes of light intensity in the opposite direction. The phenomenon above shows that there is strong competition between two modes of dual-polarized state as well as the mode jump occurs in the process of mode conversion, but there have been no specific report on this phenomenon. The longitudinal mode characteristic and the change of dual-polarized light intensity curve before and after frequency difference modulation of laser were studied. From the analysis, it is found that gain medium being only monoisotope Ne is the reason which cause the polarization abnormality of the orthogonal modes, and the influence of the monoisotopic Ne on mode competition was also expounded.