Linear GMR isolator which is profitable for transmitting analog signal was modeled and the output voltage and current in relation to the input current were investigated. GMR isolator modeling was divided into two parts, namely magnetic and electric parts. The flow chart of the modeling was drawn in which the MR curve of the spin valves were incorporated to obtain the electrical voltage output. For magnetic modeling, 3-dimensional model of planar coil was analyzed by FEM method to obtain the magnetic field strength corresponding to the input current. Coil efficiency of the planar coil having magnetic core layer was shown to have about 1.5 times larger than that of the coil without the magnetic core layer. The feedback coil current(output current) corresponding to the input coil current was calculated to be within ${pm}$0.25 mA of the linear fitting function of I$\_$out/= I$\_$in/-5 mA. Also, the response time and output waveforms were obtained when the coil current was a rectangular waveform. The rise time and fall time was 6 ${mu} extrm{s}$, respectively when the slew rate of the op-amp was 0.3 V/${mu} extrm{s}$.