Up to now, near almost optical fiber gas lasers employ/adopt the scheme of free-space coupling, which increases the difficulty to adjust the optical path, and has poor stability. All-fiber structure fiber-gas lasers are important development directions in the future. We established the numerical model of SMF-28 type tapered single-mode fiber and non-node hollow-core fiber. When the SMF-28 type single-mode fiber has a waist diameter of 40μm when the light source is LP01 fundamental mode with 1550nm wavelength, the mode field diameter is the largest. Meanwhile, we simulated that the equivalent mode field diameter of non-node anti-resonant hollow-core fiber is about 75μm at the same 1550nm wavelength light source. Then, we use different waist diameters of SMF-28 type tapered fibers injected to the non-node anti-resonant hollow-core fiber in simulation and experiments. In the scheme of the single-ended low-loss coupling, the simulation results indicate that the best waist diameter of tapered fiber is 40μm, and the calculated maximum coupling efficiency is 83.55%. Meanwhile, the experimental result of maximum coupling efficiency is 80.74% when the best waist diameter of tapered fiber is also 40μm. As for the double-ended low-loss coupling, the calculated maximum coupling efficiency is near 83.38%.