Abstract Asymmetric giant magnetoimpedance (GMI) effect in amorphous ribbons is very promising due to its possible application in developing the highly sensitive linear magnetic-field sensors. In this paper, the model of the nonlinear asymmetric volt–ampere characteristics in field-biased Co-based amorphous ribbon has been established through the time derivative of the longitudinal magnetization component in the ribbon. Its harmonics are also developed by Fourier analysis. The influence of the current amplitude on the nonlinear asymmetric effect has been studied. It is found that when the current amplitude is 8.54 mA, the sensitivity of the first harmonic voltage on the external field is equal to that of the second harmonic voltage. The results obtained are useful for developing the high-sensitive magnetic-field sensors.