High peak-to-average power ratio (PAPR) is one of the major drawbacks in the transmitted random-interleaved orthogonal frequency division multiple access (RI-OFDMA) uplink signal. The PAPR increases the complexity of analogue-to-digital (A/D) and digital-to-analogue (D/A) convertors and also reduces the efficiency of RF high-power-amplifier (HPA). This paper presents a new Discrete-Cosine transform matrix (DCTM) precoding based RI-OFDMA uplink system for high PAPR reduction. Computer simulation results show that the proposed precoding based uplink system has low PAPR as compare to those of the Walsh-Hadamard transform (WHT) precoding based RI-OFDMA uplink systems and the conventional RI-OFDMA uplink systems respectively. Additionally, the biterror-rate (BER) performance of the proposed uplink system is much better than the conventional RI-OFDMA uplink systems and at par with the WHT precoded RI-OFDMA uplink systems. Therefore, such a good improvements in both PAPR and BER offered by the proposed precoding based uplink system can notably reduce the cost and complexity of the uplink transmitter. © 2011 IEEE.