Interstitial holes are usually formed in the cladding of Photonic Crystal Fibers（PCF）in the actual drawing process.This paper presents an optical fiber in honeycomb-like lattice structure.Using the full-vector Plane Wave Expansion（PWE）method

it analyzes the bandgap properties of its circular and hexagonal cores

finds that the impacts of the core shape on the bandgap is relatively small and verifies that the Photonic Band Gap（PBG）is formed mainly due to the orderly arranged air holes in the cladding.Furthermore

it calculates and analyzes the effects of the interstitial hole diameter dint

hole pitchΛand air filling ratio fon the bandgap properties.The analog computation results indicate that in certain scope of dint

the bandgap width increases with both increasing fand reducingΛ

and the bandgap shifts towards the high frequency side.Finally

from the mode field area computation of the actually drawn fibers and the theoretical study of PBG distribution

it finds that the light in fibers in this structure mainly focuses on basemode transmission and there exist PBGs in the range of visible light waves.