Microstructure modifications are investigated for annealed Co-based amorphous ribbon in vacuum and open air. X-ray diffraction (XRD) spectra for annealed sample in vacuum indicate atomic arrangements with initial nucleation of hcp-Co crystallite at 38$0^{circ}C$ annealing temperature. However, the XRD spectra in samples with long annealing times of $t_ageq300$ min demonstrate sharp and good developed surface crystalline hcp-, fcc- Co and $Co_2$Si phases. The giant magnetoimpedance (GMI) profile at 0.1 MHz displaying one-peak behavior in vacuum annealed samples at T = 38$0^{circ}C$ irrespective of annealing time $t_a$ from 20 to 480 mim. For the annealed samples in an open air, the GMI profile shows two-peaks for $t_a$ = 20 min annealed sample. However, one of peaks disappears and an asymmetric GMI profile exhibits a drastic step-like change near zero field for $t_ageq300$min. Such asymmetric GMI characteristics is related to the surface microstructures of fcc-Co, hop-Co and $Co_2$Si crystalline phases.