We propose a hollow-core photonic bandgap fiber (HC-PBGF) with background composed of two materials to support orbital angular momentum (OAM) modes. Numerical models are set up to figure out the effective indexes and confinement losses over 1.3-2.0 μm. Simulation results show that this fiber can support more than 48 OAM modes, of which the effective indexes satisfy the condition for effective index separation (<10-4) and the confinement loss keeps under 10-7 dB/m over 1.3-2.0 μm. According to the comparison between fibers with same structure but comprising one or two background materials, adopting two materials to compose background is an effective method to significantly improve the performance of OAM-supporting HC-PBGF. The HC-PBGF proposed here is competitive in dealing for OAM multiplexing for optical communication systems.