We propose an all-fiber band-rejection filter with a tunable bandwidth, which is realized by putting a normal long-period fiber grating in series with a rotary long-period fiber grating written in a twisted single-mode fiber by CO(2) laser pulses. Bandwidth tuning is achieved by applying torsion to the composite grating. Our experimental filter shows a bandwidth tuning of approximately 16.3 nm at a rejection level of approximately 15 dB and a polarization-dependent loss lower than approximately 0.9 dB.