Digital subscriber line (DSL) systems transport high-bandwidth data, such as multimedia, to service subscribers over ordinary twisted pair copper wire telephone lines. One of the important components of the DSL system is the line driver (LD) or the power amplifier (PA). The linearity of the LD is crucial to have a high-speed internet. Any non-linearity in the LD will create intermodulation distortion and spectral regrowth that will become an obstacle to increase DSL data rate. Digital predistortion (DPD) is a known technique that can be used in order to linearize the LD and hence suppressing any nonlinear distortion. This paper considers direct predistortion of DSL-LD that is modelled using Volterra series by connecting in tandem an adaptive Volterra predistorter. The coefficients of the predistorter is recursively estimated using the Prediction Error Method (PEM). Simulation study on a LD which is modelled as 5th order Volterra system shows that the Nonlinear Filtered-x Prediction Error Method (NFxPEM) algorithm can significantly suppress spectral regrowth and converge much faster than the well-known Nonlinear Filtered-x Least Mean squares (NFxLMS) algorithm.