We demonstrate a tunable hollow waveguide distributed Bragg reflector consisting of a grating loaded slab hollow waveguide with a variable air-core. The modeling shows that a change in an air-core thickness enables a large shift of several tens of nanometers in Bragg wavelength due to a change of several percents in a propagation constant. We fabricated a slab hollow waveguide Bragg reflector with 620 mum long and, 190 nm deep 1st-order circular grating composed of SiO2, exhibiting strong Bragg reflection at 1558 nm with an air-core thickness of 10 mum for TM mode. The peak reflectivity is 65% including fiber coupling losses, the 3-dB bandwidth is 2.8 nm and the grating-induced loss is less than 0.5 dB. We demonstrate a 3 nm wavelength tuning of the fabricated hollow waveguide Bragg reflector by changing an air-core thickness from 10 mum to 7.9 mum.