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A companding technique is proposed to reduce the peak-to-average-power ratio of the orthogonal frequency division multiplexing (OFDM) signal in this paper. The probability density function of the amplitude of the OFDM signal is determined. Because of the Gaussian distribution of the OFDM signal, the companding technique can be quite effective, since a large OFDM signal only occurs infrequently. The peak-to-average power ratio of an OFDM system and the optimal companding coefficient are determined in this paper. The symbol error rate of the systems after the companding is derived. The performances of the system with and without the companding are also compared.