The Compensated Horner Scheme is an accurate and fast algorithm to evaluate univariate polynomials in floating-point arithmetic. The accuracy of the computed result is similar to the one given by the Horner scheme computed in twice the working precision. This Compensated Horner Scheme runs at least as fast as existing implementations producing the same output accuracy. In this talk, we will present a parallel version of the Compensated Horner Scheme. Some experiments on multicore and Graphics Processor Units (GPU) architectures will be presented to show the efficiency of this algorithm.