Abstract: To further reduce the imaging time and improve the image quality, an improved GRAPPA algorithm of finite impulse response (FIR) is presented. Compared with the conventional GRAPPA algorithms with fixed weights, the proposed algorithm considers the phase change of the weighted coefficients, has a better description for the correlation of k-space data, and is more consistent with the physical process of data fitting for parallel imaging. To demonstrate the validity of the improved algorithm, the simulation experiments were performed with the original data of brain and cardiac images. The reconstructed images and the mean square error (MSE) were obtained with a higher acceleration factor, and were compared with the conventional and other GRAPPA algorithms. The results show that the reconstructed images are clearer and the MSE value are much smaller using the proposed algorithm. Therefore, the improved k-space data acquisition algorithm is effective and feasible.