To meet the growing demand for communication channel capacity, various types of space division multiplexing (SDM) transmission fiber have been proposed. In this paper, a novel hole-walled six core fiber (MCF) structure is introduce and first three LP core modes (LP01, LP11a and LP11b) modes are studied. These two modes are very important for long distance optical fiber communication. Some supported higher order cladding modes are also presented and very peculiar field distributions can be found. Results are compared with normal step-index six core MCF structure. It is found that cladding modes can be greatly suppressed with hole-walled structure. This study also includes the coupling between LP01 mode and one higher order cladding mode under periodic perturbation conditions. © 2020 IEEE.