The proposed work presents a combination of GRAPPA and Compressed sensing (POCS) to reconstruct MR images from the highly under-sampled data. Firstly, GRAPPA is applied to the acquired under-sampled data. The output of GRAPPA which contains aliasing artifacts (especially for high acceleration factors) is fed in to POCS which solves for the solution image iteratively and produces a reconstructed image with minimal aliasing artifacts. The reconstruction results are compared with GRAPPA and POCS separately. The results show that the proposed method significantly reduces the aliasing artifacts as compared to GRAPPA or POCS reconstructions.