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A novel adaptive companding transform scheme is proposed to efficaciously reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) signals. The feasible adaptive companding algorithm is proposed and discussed too. The computer simulation based on MATLAB shows that the PAPR is reduced efficiently by using this scheme, and it has little effect on the performance of the system. Furthermore, the prospective targets, both the PAPR and the performance of system, can be satisfied simultaneously by adjusting the parameter of companding 'automatically. It realizes the optimal tradeoff between PAPR reduction and the performance of system simultaneously.