We propose the integration of a tapered spot-size converter for coupling between a narrow air-core hollow waveguide and a single-mode fiber (SMF). The linear taper waveguide consisting of SiO₂ is integrated with a hollow waveguide composed of highly reflective multilayer mirrors. Light is guided with total internal reflections at a SiO₂ taper surface and the multiple reflections in the multilayer mirror. The core thickness of a taper SiO₂ waveguide is linearly changed from 15µm to 0.6µm. The modeling result shows a coupling loss of less than 1dB between a SMF and a hollow waveguide with an air-core thickness of 1µm. A taper waveguide-induced loss is less than 0.1dB for a two-dimensional linear taper waveguide with a length of less than 1mm. Using the proposed structure, we can expect the dramatic reduction in coupling losses by 10dB. The device structure can be formed by fully planar fabrication processes based on lithography, etching and coating. The proposed spot-size converter enables us to achieve a large tunability of over 10% in propagation constant in hollow waveguides with a variable air-core.