The primary limitation in non-Cartesian spiral imaging is blurring from off-resonance effects. Blurring, however, scales with the readout duration and can be greatly reduced by the use of parallel MRI (pMRI) methods. Unfortunately pMRI reconstructions are non-trivial in the case of spiral trajectories [1-3]. In this study, we have focused on the implementation of a fast reconstruction algorithm for parallel imaging with spiral trajectories, which enables single-shot spiral pMRI. As in other recent approaches [4,5] for parallel imaging of nonCartesian k-space sampling by means of the GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) algorithm [6], the proposed algorithm works completely in k-space leading to significantly reduced reconstruction times.