A new type of Bragg fibers,i.e. hollow-core cobweb-structured optical fibers,which can be used to the low-loss transmission from visible to near infrared region (0.65 μm-1.55 μm),terahertz wave (200 μm-480 μm) and circular-polarization-maintaining single-mode transmission are investigated. Results show that the hollow-core cobweb-structured fibers have less loss than other hollow-core Bragg fibers. The fibers can be constituted by using the plastics or glasses with large absorption losses.