This paper presents a low-loss fusion splice method between the nested hollow-core anti-resonant fiber (HC-ARF) and single-mode fiber (SMF) by introducing a graded-index multi-mode fiber (GIMF) as a transition fiber. The mode field matching between the nested HC-ARF and the SMF is achieved by using the GIMF as the mode field adapting fiber and expanding the mode field in the SMF by using its self-imaging effect. The effects of discharge time and discharge power on fusion splice loss during fusion splicing are explored in the experiments. Based on an optimized fusion splicing scheme, the integrity of the microstructure of the nested HC-ARF fusion splicing end face is effectively protected, and the average fusion splicing loss is as low as 0.60 dB. The experimental results provide a reference to improve the compatibility of the nested hollow-core anti-resonant fibers with the existing fiber system.