The influence of Bragg fiber design parameters on photonic bandgap was discussed via the finite element method. The theoretical results show that the bandgap move to long wavelength when the thickness or the refractive index of the Ge-doped layers increases. A novel W-shape-core Bragg fiber was firstly proposed by introducing a F-doped low index layer adjacent of fiber core. The calculation demonstrates the W-shape-core Bragg fiber can reduce the confinement loss and improve the bending-resistant ability effectively. A W-shape-core Bragg fiber was designed with a core diameter of 30 μm, which has a loss of 0.1 dB/km at wavelength of 1.06 μm and is proved single mode propagation theoretically.