The photonic bandgap structure for a photonic crystal with rounded hexagons air hole arranged by triangular lattice was calculated by plane wave method (PWM), and based on the structure diagram, structure parameters of a seven-cell hollow-core photonic bandgap fiber (PBF) was designed to propagate a lightwave with λ=1.55 μm. And then numerical simulation for a hollow-core PBF with a silica ring introduced at the core-cladding interface was done with full-vectorial finite element method (FEM), and the intensity distribution, intensity contour distribution in z axis and a curve of leakage loss as a function of normalized core thickness were presented. The ranges of out core radius and the normalized thickness of a silica ring for the fiber free of surface modes and reducing loss are 1.55Λ～1.7Λ and 1.3～1.5 or 3.4～3.8 respectively. A silica ring can not only create surface modes but also remove surface modes, which depends on choices of the out core radius and a silica ring thickness.