The hollow core anti resonant and photonic bandgap hybrid fiber is a new type of hollow core microstructure fiber which has just emerged recently.Due to this optical fiber can realize the characteristics of low loss and single mode transmission at the same time,so it can be used in fiber optic gyro,fiber laser communication and other fields.In order to achieve good single mode performance and low loss,the confinement and scattering losses of the fundamental and higher order modes of this kind of fiber are calculated in this paper.By optimizing the normalized inner diameter d/D of the inner cladding pore and the thickness t of inner cladding airhole,good single mode performance and low loss are achieved in the operating wavelength range 1500～1590 nm for d/D=0.68 and t=500 nm for hollow core anti resonant and photonic bandgap composite fibers.