Hollow-core fibers (HCFs) have been under intense research interest thanks to their many advantages including low latency, low nonlinearity, and temperature insensitivity. The most recent progress on the double nested antiresonant nodeless fiber (DNANF) demonstrated fiber losses of only 0.174 dB/km. Transmission of ultra-short, high-peak-power pulses can greatly benefit from low nonlinearity of HCFs. However, the waveguide dispersion in HCFs such as DNANF is typically 2-3 ps/(nm·km) in the low-loss transmission region, still causing unwanted pulses broadening. Here, we demonstrate a low-loss interconnection between HCF and a dispersion-compensating fiber (DCF), enabling to obtain HCF+DCF link with zero-net dispersion. To adapt the relatively small mode-filed diameter (MFD) of DCF (4.9 μm) to the MFD of the HCF, we first splice a short segment of graded-index (GRIN) multi-mode fiber on the DCF. The GRIN fiber is then polished to a specific length to obtain an optimal MFD adaptation to our HCF, which was a nested antiresonant nodeless fiber (NANF) with 26.3 μm MFD at 1550 nm. We obtained a loss of only 0.55 dB for the whole DCF-GRIN-NANF component. By depositing an anti-reflective coating on the mode-field adapter end-face, the interconnection loss can be further reduced to 0.39 dB.