The highly sensitive giant magneto-impedance effect in a solenoid containing a magnetic core of Fe36Co36Nb4Si4.sB19.2 （FeCo-based） ribbon under a weak magnetic field （WMF） is presented in this paper. The FeCo-based amorphous ribbon is prepared by single roller quenching and annealed with Joule heat in a flowing nitro- gen atmosphere. The giant magnetoimpedance effect in solenoid （GMIES） profiles are measured with an HP4294A impedance analyzer. The result shows that the CMIES responds to the WMF sensitively （as high as 1580 %/A.m-1）. The high sensitivity can be obtained in a moderate narrow range of annealing current density （30-34 A/mm2） and closely depends on the driven current frequency. The highest sensitivity （1580 %/A.m-1） is obtained when the FeCo- based amorphous ribbon is annealed at 32 A/mm2 for 10 min and then driven with an alterning current （AC） at the frequency of 350 kHz. The highly sensitive GMIES under the WMF may result from the multiple magnetic-anisotropic structure, which is induced by the temperature gradient produced during Joule-heating the ribbon.
