The paper presents the novel concept of the magnetoelectric sensor constructed using the amorphous glass ribbon. Its output characteristics (voltage pattern), conditions of work and experimental results are presented. The novel construction allows for minimizing the demagnetizing field in the core of the sensor and linearization of the characteristics between the magnetic field and obtained voltage. Conducted experiments were aimed at determining the sensor operation in the presence of the constant magnetic field (HDC). The main concern of the tests was to verify the linear dependency between the HDC value and the amplitude of the output voltage. Next, the computer model representing the sensor behavior in the constant magnetic field is described. The model implements the parameter identification task based on the regression algorithms. The presented work shows that the proposed device can be used to measure the weak magnetic field and the dependency between the output signal amplitudes and the constant component in the measured magnetic field is approximately linear. This enables measurements of even weak fields.