The guided-mode properties of hollow-core photonic crystal fibers (HC-PCFs) were studied with the plane-wave expansion method (PWE). The simulation results show that, for a given wavelength in the photonic band-gap of the cladding structure, stable fundamental core mode may be obtained only with specific vertical phase propagating constants. Moreover, the mode field distributions of fundamental core modes depend on the wavelength. When the wavelength is right at the center of the fundamental core mode transmitting curve, the mode field may be confined in the air-core perfectly. When the wavelength is near the edges of the fundamental core mode transmitting curve, the energy of guided-wave core modes may leak into the cladding of HC-PCF.