The μ-law companding function has been applied widely in orthogonal frequency division multiplexing (OFDM) to reduce the peak-to-average power ratio (PAPR). How-ever, nonlinear distortion caused by the μ-law companding function is considered a key im-pairment in OFDM communication systems. Few studies have addressed theoretical non-linear distortion caused by μ-law companding function for OFDM systems. In this paper, we derive a closed-form expression of signal distortion as well as the closed-form bit error rate (BER) of OFDM system caused by the μ-law companding function. Based on the the-oretical signal distortion and BER expression, the theoretical BER value and signal distortion value can also be calculated, which can guide us to choose appropriate μ value for different BER condition and bit-to-noise (Eb/N0) condi-tion efficiently. Then the PAPR performance can also be predicted. The results show good agreement on the Monte-Carlo simulation results and the obtained theoretical BER re-sults. Furthermore, based on theoretical signal distortion and theoretical BER expression, the figure of the relationship among BER value, Eb/N0 and μ is also given. Based on this figure, we can find the appropriate μ law for different BER and Eb/N0 condition. And then the PAPR performance can also be predicted.