The design of all-solid photonic bandgap fibers based on a high-index broken ring is investigated, where the background material is silica and the broken ring consists of several individual high-index rods. Density of states maps and Bloch mode field distributions obtained by plane wave expansion method show that a high-order bandgap in such fibers can be engineered and broadened. The principle is that both the azimuthal and the radial orders of the LP modes of the high-index rods in the cladding can be controlled by the broken ring. It is demonstrated that the highest azimuthal order of the group of less affected LP modes is determined by the rod number and the bandgap width is largely affected by the rod size. The high-order bandgap can be used to design all-solid photonic bandgap fiber with broad transmission ranges of 488 nm and 944 nm for a center wavelength of 800 nm and 1550 nm, respectively, and the transmission window features the typical normal-zero-anomalous dispersion profile.