A giant magnetoimpedance sensor with a step-like impedance property was obtained in the case of amorphous Co₈₅Nb₁₂Zr₃ soft magnetic thin film in a rectangle shape with an in-plane uniaxial easy axis in a direction nearly 60 degrees relative to the width direction of the element. It was shown experimentally that the magnetic field in which the step-like impedance change occurs has an almost constant value with a standard deviation in the microtesra (μT) range. The magnetic field in which the step-like change occurs includes information on the external magnetic field. To realize a magnetic field sensor with an accuracy of nT/Hz^1/2 by using this step-like phenomenon, a differential circuit was studied in combination with an alternating bias field in the kilohertz (kHz) frequency range. The aim of the differential circuit was to make the driving circuit into a digital logic circuit, by using pulse signals timed to coincide with the step-like changes. The alternating bias field increases the sampling number, because of the step-like changes in the bias frequency. The aim of the ac bias is to improve the sensor accuracy by using an averaging effect. This paper reports a first trial of the method. As a result, a high-linearity sensor without hysteresis was obtained, which had a linearity error of less than 0.5% in the range of ±100 μT. A measurement accuracy of 460 nT was achieved with a 20 Hz time constant of the output low pass filter (LPF).