Wideband-adjustable band-rejection filters based on chirped and tilted fiber Bragg gratings (CTFBG) are proposed and experimentally demonstrated. The flexible chirp-rate and wide tilt-angle provide the gratings with broadband filtering functions over a large range of bandwidths (from 10 nm to 150 nm), together with a low insertion loss (less than 1 dB) and a negligible back-reflection (lower than -20 dB). The slope profile of CTFBG in transmission can be easily tailored by adjusting the tilt angle, grating irradiation time and chirp rate-grating factor, and it is insensitive to the polarization state of the input light, as well as to temperature, axial strain and surrounding refractive index. Furthermore, by coating the CTFBG with a suitable polymer (whose refractive index is close to that of the cladding glass), the cladding modes no longer form weakly discrete resonances and leave a smoothly varying attenuation spectrum for high-quality band-rejection filters, edge filters and gain equalizers.