High-performance FFT processor is indispensable for real-time OFDM communication systems. This paper presents a CORDIC based design of variable-length FFT processor which can perform various FFT lengths of 64/128/256/512/1024/2048/4096/8192-point. The proposed FFT processor employs memory based architecture in which mixed radix 4/2 algorithm, pipelined CORDIC, and conflict-free parallel memory access scheme are exploited. Besides, the CORDIC rotation angles are generated internally based on the transform of butterfly counter, which eliminates the need of ROM making it memory-efficient. The proposed architecture has a lower hardware complexity because it is ROM-free and with no dedicated complex multiplier. We implemented the proposed FFT processor and verified it on FPGA development platform. Additionally, the processor is also synthesized in 0.18μm technology, the core area of the processor is 3.47mm² and the maximum operating frequency can be up to 500MHz. The proposed FFT processor is better trade off performance and hardware overhead, and it can meet the speed requirement of most modern OFDM system, such as IEEE 802.11n, WiMax, 3GPP-LTE and DVB-T/H.