In this paper, we propose a new OFDM system for an IIR channel with the form of $B(z)/A(z)$ for two polynomials $A(z)$ and $B(z)$. Different from the conventional OFDM transmission over an FIR channel, a guard interval of an OFDM symbol is added such that the corresponding part at receiver is the cyclic prefix (CP) of the received OFDM symbol. The guard interval and CP lengths are the same and not smaller than the orders of polynomials $A(z)$ and $B(z)$. The OFDM symbol without the guard interval is the same as the conventional OFDM symbol without the CP. At the receiver, the IIR channel is then converted to $N$ intersymbol interference (ISI) free subchannels, where $N$ is the number of subcarriers of an OFDM symbol.