Companding is an effective method for peak-to-average power ratio (PAPR) reduction in orthogonal frequency division multiplexing. In this paper, the universal design criterion of companding scheme is introduced by analyzing signal distribution transformation and corresponding signal distortion. In addition, according to the constraints of the proposed criterion, a new companding scheme is designed. By compressing the signals to the target distribution, this scheme can effectively reduce the signal PAPR while achieving good bit error rate and power spectral density performance. Theoretical analysis and simulation results demonstrate the effectiveness of the proposed design criterion and scheme.