In this paper, we propose a cost-effective and low-power 64-point fast Fourier transform (FFT)/inverse FFT (IFFT) architecture and chip adopting the retrenched 8-point FFT/IFFT (R8-FFT) unit and an efficient data-swapping method based output buffer unit The whole chip systematic performance concerning about the area, power, latency and pending cycles for the application of IEEE 802.11a WLAN standard has been analyzed. The proposed R8-FFT unit utilizing the symmetry property of the matrix decomposition achieves half computation-complexity and less power consumption compared with the recently proposed FFT/IFFT designs. On the other hand, applying the proposed data-swapping method, a low-cost and low-power output buffer can be obtained. So as to further increase system performance, we propose one scheme: the multiplication-afler-write (MAW) method. Applying MA W method with R8-FFT unit, the resulting FFT/IFFT design not only leads to the balancing pending cycle, but also abbreviating computation latency to 8 clock cycles. Consequently, adopting the above proposed two units and one scheme, the whole chip consumes 22.36mW under 1.2V@20 MHz in TSMC 0.13 1P8M CMOS process.