In this paper, combining the parallel combinatory (PC) code and the a flexible OFDM structure [7], we report the design of a new OFDM system with PC code for various applications with a moderate transmission rate. The system can select appropriate phase sets for all modulated subcarriers for each PC code for different design requirements such as peak-to-average power ratio (PAPR) reduction or HER performance improvement. The proposed system will achieve better PAPR characteristics and promising HER performance. In addition, due to the flexible OFDM structure, the proposed PC-OFDM system will also have properties of high adaptability and compatibility.