To study the transmission ability of hollow-core anti-resonance fiber, a mid-infrared laser transmission experiment was carried out using a self-made nodeless hollow-core anti-resonance fiber from 2.6 μm to 4.35 μm spectral region. The fiber cladding consists of seven silica capillary tubes, the average wall thickness is 800 nm, the outer diameter of the fiber is 365 μm, and the core diameter is 115 μm. A tunable mid-infrared source was used as a broadband light source. The laser propagation capability of the fiber at 2.60 μm, 3.27 μm, 3.41 μm, 3.80 μm, 4.08 μm, 4.21 μm, and 4.35 μm was tested. And the transmission loss at this spectral region of the fiber was measured. Results show that the fiber can realize low-loss light guide from 2.6 μm to 4.08 μm band, with the lowest transmission loss of 0.037 dB/m at 3.27 μm. The transmission loss of the fiber is 3.200 dB/m at 4.08 μm and 0.788 dB/m at 4.35 μm, where the attenuation of bulk silica is 1000 dB/m and 3000 dB/m, respectively. Hollow-core anti-resonance fiber has great potential in the application of mid-infrared laser flexible delivery.