We have presented herein the results of microstructure, surface magnetic domains (SMDs), and giant magneto-impedance (GMI) effect of melt-extracted Co68.15Fe4.35Si12.25B11.25Nb2Cu2 amorphous wires for the first time employed by using a cryogenic Joule annealing (CJA) technique with large DC current amplitude. Compared with the conventional JA method, experimental results indicate that the maximum GMI ratio [ΔZ/Z0]max achieves up to 425% at 8.1 MHz with monotonic increase of the axial magnetic field Hex up to 6.5 Oe for 300 mA (equal to around 1.06 × 106 A/dm−2) CJA-ed wire, which is about 75% larger than the [ΔZ/Z0]max for the 100 mA (nearly 3.53 × 105 A/dm−2) JA-ed microwires. The remarkable features of large and linearly sensitive response field (2.5 ∼ 6.5 Oe) and the sensitivity of 99.4%/Oe with higher GMI ratio simultaneously make the CJA tailored melt-extracted microwires promising candidate materials for miniaturized GMI sensors. Another interesting result of GMI profiles of 200 mA (appropriately equal to 7.07 × 105 A/dm−2) CJA-ed wire show a linear response to Hex (ranging from 10 to 80 Oe or more), this behavior of GMI curves can be explored to fabricate bi-sensor. Large response field proves to originate from the intensive coupling between the radial stress field and the circumferential magnetic field during CJA process. The effect of outer-shell microstructure and complex SMD for 300 mA CJA-ed microwire is attributed to the fact that liquid nitrogen hinders the evolution of circumferential domain structure to some extent and protects the amorphous structure in the shell region.