This paper presents a parallel Salt and Pepper (SP) noise removal algorithm in a grey level digital image based on the Hypergraph Based Root Mean Square (HGRMS) approach. HGRMS is generic algorithm for identifying noisy pixels in any digital image using a two level hierarchical serial approach. However, for SP noise removal, we reduce this algorithm to a parallel model by introducing a cardinality matrix and an iteration factor, k, which helps us reduce the dependencies in the existing approach. We also observe that the performance of the serial implementation is better on smaller images, but once the threshold is achieved in terms of image resolution, its computational complexity increases drastically. We test P- HGRMS using standard images from the Berkeley Segmentation dataset on NVIDIAs Compute Unified Device Architecture (CUDA) for noise identification and attenuation. We also compare the noise removal efficiency of the proposed algorithm using Peak Signal to Noise Ratio (PSNR) to the existing approach. P-HGRMS maintains the noise removal efficiency and outperforms its sequential counterpart by 6 to 18 times (6x - 18x) in computational efficiency.