This paper proposes a high-speed and area-efficient FFT algorithm and performs a hardware implementation. This algorithm, named by "Radix-4/2", uses the feature of existing radix-2^3 algorithm, It reduces the number of non-trivial multipliers in SFG to the ratio of 3 to 2 compared with radix-2 or radix-4 algorithm and radix-4/2 has also twice throughput as radix-2^3 algorithm's. It is proved that FFT processor using the proposed algorithm and 64-point MDC pipeline architecture has twice throughput as radix-2^3 algorithm's, and reduces areas by 25 percentages in contrast to radix-4 algorithm's.