The resonant wavelength of long-period fiber grating (LPFG) coated with sensitive film,whose refractive index varies with the surrounding medium,changes with the film refractive index.When the coupling strength of LPFG with non-absorbing film coating is π/2,the loss peak corresponding to the resonance wavelength gets to zero.However,it is not the case for the LPFG coated with complex refractive index film.When the coupling strength of LPFG with complex refractive index film is π/2,the loss peak is not zero.While the resonant wavelength is sensitive to the film refractive index,imaginary part of propagation constant of clad mode becomes larger,which causes reduction or even disappearance of the loss peak.It is not conducive to the measurement of resonant wavelength.Analytical solution of the value of the loss peak is obtained by solving the coupled-mode equations for LPFG with complex refractive index film.The condition under which loss peak gets to zero is found.Designing LPFG according this principle,the unfavorable factor mentioned above can be effectively avoided.