An apparatus of sensing a magnetic field using a ceramic superconductor magneto-resistive element having a superconductor magneto resistive effect of non linear characteristic against the applied magnetic field, there is provided a coil for applying a bias magnetic field to the magneto-resistive element, the coil is connected to a feed back power source for supplying current for holding the output of the magneto-resistive element constant value, whereby the applied magnetic field is measured by the current supplied to the coil.There is disclosed also a device for sensing a magnetic field using a magneto-resistive element comprising a superconductor member having weak coupling grain boundaries, said device comprising means for applying A.C. bias magnetic field to said element, and means for taking out an output voltage of the element generated by application of the bias magnetic field as the signal representing the intensity of the applied magnetic field.