A chipless, wireless current sensor system was developed using a giant magnetoimpedance (GMI) magnetic sensor and one-port surface acoustic wave (SAW) reflective delay line for real-time power monitoring in a current-carrying conductor. The GMI sensor has a high-quality crystalline structure in each layer, which contributes to a high sensitivity and good linearity in a magnetic field of 3-16 Oe. A 400 MHz RF energy generated from the interdigital transducer (IDT)-type reflector on the one-port SAW delay line was used as an activation source for the GMI magnetic sensor. The one-port SAW delay line replaces the presently existing transceiver system, which is composed of thousands of transistors, thus enabling chipless and wireless operation. We confirmed a large variation in the amplitude of the SAW reflection peak with a change in the impedance of the GMI sensor caused by the current flow through the conductor. Good linearity and sensitivity of ~0.691 dB/A were observed for currents in the range 1-12 A. Coupling of Mode (COM) modeling and impedance matching analysis were also performed to predict the device performance in advance and these were compared with the experimental results.