Generalized autocalibrating partially parallel acquisitions (GRAPPA) is a k-space-based magnetic resonance imaging (MRI) reconstruction algorithm that obtains coefficients by acquiring k-space center data with the Nyquist frequency requirement, fitting these data as auto-calibration signal (ACS). The under-sampled k-space data are then filled using the linear correlation of the neighboring points of the k-space. At high reduction factors, images reconstructed by using GRAPPA have high levels of noise even when the number of ACS lines is significantly increased. NL-GRAPPA (Non-linear GRAPPA) can improve GRAPPA for a comparatively impressive image quality. However, it is extremely difficult to reduce the sampling time significantly because of the high number of ACS lines that must be sampled. In this paper, we proposed an undersampling parallel MRI (pMRI) reconstruction technique based on the ideology of normal distribution to improve the traditional GRAPPA and NL-GRAPPA methods. The proposed method mainly takes advantage of the fact that the data in the center of the k-space had a greater impact on the imaging quality than the data at the edges, and then samples the data based on the ideology of normal distribution, i.e., discarding part of the data at the edges of the k-space. The experimental results show that our proposed method can significantly reduce the number of sampled lines and have higher imaging quality with a lower number of ACS lines.