The characteristics of magnetohydrodynamics (MHD) stability of plasmas with the internal diffusion barrier (IDB) are intensively studied in the Large Helical Device (LHD) experiment. These plasma are produced by the rapid fueling into the core region with pellet injection. As a result, a high electron pressure due to the large central electron density ($n_e(0) ~ 10^{21}[m^{-3}]$) is attained. A steep pressure gradient appears within the core region and a gentle gradient exists in the peripheral region. In spite of the steep gradient, ideal and resistive MHD modes in the core region are stable. On the other hand, the resistive MHD mode which is investigated with the MHD turbulent transport model becomes unstable in the peripheral region where the pressure gradient is gentle. The formation of such pressure profile with a steep gradient is characterized by a time evolution of an electron density profile after the pellet injection. The electron density within the core region decreases at a slower rate than that of the peripheral region. These theoretical results and experimental observations suggest that the formation of the electron density of the IDB plasma is influenced by the resistive MHD mode rather than the ideal MHD mode.