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We have found periodic oscillations in the Josephson-vortex flow resistance of the intrinsic Josephson junctions of Bi2Sr2CaCu2O8+δ single crystal under the parallel magnetic fields from a few kOe to more than 70 kOe. The oscillations indicate a precise and an absolute measurement at higher fields. To demonstrate the characteristics of the magnetic sensor, we have performed modulation measurements with small coils producing a few Oe in Tesla order magnetic fields and have studied details on the flow resistance in the magnetic field and temperature cycles. The results show a high performance as a magnetic sensor.