In a wireless communications system, a predistorter is often used to compensate for the nonlinear distortions that result from operating a power amplifier near the saturation region, thereby improving system performance and increasing the spectral efficiency for the communication channels. This paper presents a new VLSI design for the polynomial digital predistorter (DPD). The proposed DPD uses a Coordinate Rotation Digital Computing (CORDIC) processor and a PD process with a fully-pipelined architecture. Due to its simple and regular structure, it can be a competitive design when compared to existing polynomial-type and approximated DPDs. Implementing a fifth-order distorter with the proposed design requires only 43,000 logic gates in a $0.35{mu}m$ CMOS standard cell library.