We study the eigenstates of Kramers-Henneberger (KH) hydrogen atom with σ_g and σ_u symmetries in a linearly polarized high-frequency strong laser field, within the framework of the nonperturbative theory. The theory predicts that within high-frequency limit, electric structure is determined by a time-independent Schr?dinger equation containing a “dressed” Coulomb potential. We use a new basis set to solve the structure equation and compare our calculation results with existing research results. Our results are accurate for low-level eigenstates especially the ground state (1s). But for excited states, our results are accurate only when the laser intensity is high. Furthermore, we also study the eigenstate structures of KH hydrogen atom. We find when the laser intensity is high, not only the low-level eigenstates exhibit the “dichotomy” structures, but also the high-level eigenstates display “muti-lobe” structures.