A dual-core photonic crystal fiber based on total internal refraction and photonic bandgap effect simultaneously is proposed,and its coupling properties are investigated by use of a full-vector finite element method. It is found that the coupling between the two cores of this photonic crystal fiber is different from that of other fibers based on single light-guiding mechanism. This fiber presents novel phenomena such as alternative cutoff of odd and even supermodes,existence of coupling length maxima and so on. The resonance of high-index inclusion between the two cores plays an important role in the coupling. The coupling length of the fiber can be changed significantly by tuning the sizes of air holes and distance between two air holes,and the locations of coupling length maxima can be shifted by adjusting the refractive index of high-index inclusion.