A multi-carrier modulation technique is Orthogonal Frequency Division Multiplexing (OFDM) which divides the available spectrum into many carriers. The spectrum efficiently uses in OFDM compared to FDMA by spacing the channels much closer together. All carriers in OFDM orthogonal to one another to prevent interference between the closely spaced carriers. The objective of this work is to study and design a basic OFDM modulator and demodulator which contain FFT (Fast Fourier Transform) and IFFT (Inverse Fast Fourier Transform), mapping block (QAM), De-mapping block, serial to parallel and parallel to serial converter using hardware programming language (VHDL). In OFDM system IFFT/FFT processor is designed based on pipelined architecture. The pipeline architecture hold so good so as to reduce the huge structure of FFT/IFFT processor. In this work radix-22 algorithm and radix-22 architecture is used to design FFT processor. The design has been written in VHDL language and then simulated in the Xilinx ISE simulator 14.2 software and finally implement the designed in FPGA board (SPARTAN 3E starter kit).