The liquid-core fiber with relatively high refractive index difference between the core and cladding is proven to be bending insensitive. The single mode condition and bending loss of the fiber with a mixture of toluene and chloroform as its core material are studied. The results show that the bending loss of this fiber is not only much smaller than the conventional silica single mode fiber but also can be tuned by the temperature and liquid mixture ratio. This kind of fiber may find its potential applications in all-optical network.