FeCuNbSiB and FeZrBCu nanocrystalline ribbons can be obtained directly through the melt- spinning technique without additional annealing processes. The giant magnetoimpedance can be observed in FeCuNbSiB and FeZrBCu as quenched ribbons. The addition of Cu improves the nano-crystallization of alpha-Fe(Si) or alpha-Fe phase and reduces the grain size in FeCuNbSiB and FeZrBCu as quenched ribbons, which enhances the magnetoimpedance via increasing the variation of permeability under fields. The present experimental results reveal a novel route to fabricate the Fe based nanocrystalline soft magnetic materials with giant magnetoimpedance effect.