Mode is the fundamental concept in fiber optics, which is one of the most concerned issues in the fiber laser research. However, the mode degeneracy issue has not been clarified in common literature. By the classical electromagnetic theory, the degeneracy of vector mode and linearly polarized modes was analyzed and the relation between vector mode and linearly polarized mode were discussed in this paper. In the weakly guiding step index fiber, the vector mode and the linearly polarized mode were both the orthogonal complete basis for describing the optical field. The optical field described by vector mode [HE_1n^(o)、HE_1n^(e)] and linearly polarized mode [LP_0n^(ye)、LP_0n^(xe)] were 2 dimensional; the optical field described by vector mode [TE_0n、HE_2n^(o)、HE_2n^(e)、TM_0n]] and linearly polarized mode [LP_1n^(yo)、LP_1n^(ye)、LP_1n^(xo)、LP_1n^(xe)] were 4 dimensional; the optical field described by vector mode [EH_m-1n^(o), EH_m-1n^(e), HE_m+1n^(o), HE_m+1n^(e)] and linearly polarized mode [LP_mn^(yo), LP_mn^(ye), LP_mn^(xo), LP_mn^(xe)] were 4 dimensional.