The demand to lattice-based cryptographic schemes has been inreasing. Due to processing unit having multiple processors, there is a need to implements such protocols on these platforms. Graphical processing units (GPU) have attracted so much attention. In this paper, polynomial multiplication algorithms, having a very important role in lattice-based cryptographic schemes, are implemented on a GPU (NVIDIA Quadro 600) using the CUDA platform. FFT-based and schoolbook multiplication methods are implemented in serial and parallel way and a timing comparison for these techniques is given. It's concluded that for the polynomials whose degrees are up to 2000 the fastest polynomial multiplication method is iterative NTT.