For compressed sensing magnetic resonance imaging, algorithms plays a significant role in sparse reconstruction. The Projected Fast Iterative Soft-thresholding Algorithm (pFISTA), a simple and efficient algorithm solving sparse reconstruction models, has been successfully extended to parallel imaging. However, its convergence criterion still poses as an open question, yielding no guideline for parameter setting that allows faithful results. In this work, we prove the sufficient conditions for the convergence of parallel imaging version of pFISTA. Results on in vivo data demonstrate the validity of the convergence criterion.