A long period fiber grating (LPFG) is a band rejection fiber device with periodical retractive index modulation formed along the axis of the fiber core. Different with a fiber Bragg grating (FBG), it couples light from the forward propagating fundamental core mode into co propagating cladding modes at discrete wavelengths. Dependences of effective indices for fundamental core mode and cladding modes (HE1l/EH1l) upon wavelength, and the coupling constants between fundamental core mode and cladding modes (HE1l/EH1l) are studied. It is found that effective refractive indices for the core mode and cladding modes of LPFG both decrease with wavelength. Coupling constant formed with HE1l mode is much greater than that with EH 1l mode. Also coupling constants increase with the order of cladding modes at the lowest few ones. These differ with the conclusions drawn before.