A coated long-period fiber grating (LPFG) operating at the phase-matching turning point couples the fundamental core mode to a higher-order cladding mode, producing a single broad-band whose 3dB-bandwidth is dependent on the difference in dispersion between the core mode and a cladding mode, grating length and central wavelength. The variations of film refractive index and thickness influence the difference in dispersion between the core mode and cladding mode and thus, the bandwidth of loss peak. The central wavelength of loss peak also varies with the changes of film parameters. When the film refractive index is 1.57 and the film thickness is 350 nm, the bandwidth of loss peak reaches 302 nm. The bandwidth can be further improved to 334 nm by reducing the grating length based on the fact that the loss at the central wavelength is guaranteed to be more than 6 dB. A further investigation shows that introducing a π phase shift into a uniform LPFG at a proper position that is away from the grating center can increase the bandwidth to 372 nm and more.