High peak-to-average power ratio (PAPR) is the biggest problem of orthogonal frequency division multiplexing (OFDM) systems. To compensate this problem, we suggested a technique that is based on the combination of discrete Fourier transform (DFT) and root-based nonlinear companding. Since DFT precoding is a linear technique, it reduces PAPR by distorting the phase with minimum system complexity. Moreover, root-based μ-law companding (RMC) is also adopted to further minimize PAPR by changing probability density function from Rayleigh distribution that OFDM signals follow. By knowing that standard μ-law companding (MC) only enlarges the low amplitude of the signals and does not influence high peaks. However, RMC not only expands low-power signals but also compresses higher amplitude of the OFDM signals simultaneously unlike standard MC. In comparison to other mentioned techniques, the proposed technique (DFT-precoded RMC) accomplishes significant PAPR minimization of the OFDM systems. When complementary cumulative distribution function  =  10^−  4, the proposed technique reduces PAPR up to 1.98 and 1.99 dB for subcarriers N  =  128 and subcarriers N  =  256 quadrature phase shift keying (QPSK)-based OFDM system, respectively. At an error probability of ^{10  −  4}, the bit error rate (BER) performance of the proposed technique improves by 0.23 and 0.18 dB over Anoh et al.’s technique for subcarriers N  =  128 and N  =  256, QPSK, and additive white Gaussian noise channel, respectively. Also, for multipath Rayleigh fading channel, the BER performance of the proposed technique is improved over Anoh et al.’s and RMC techniques at the same BER.