The local k-space neighborhood model is a recently proposed k-space low-rank constrained reconstruction model, which uses the linear displacement invariance of the image to map the k-space data of the image to a high-dimensional matrix, which can solve the problem of image reconstruction. In the process of parallel magnetic resonance imaging reconstruction, the use of undersampling technology to increase the imaging speed will cause the quality of the reconstructed image to decrease. For this reason, a local k-space neighborhood modeling algorithm based on L_p-norm joint total variational regular terms is proposed. The proposed algorithm is to experiment with the proposed algorithm and other algorithms on the human brain and knee datasets. The experimental results show that compared with other algorithms, the proposed algorithm can reduce the artifacts of the reconstructed image, retain the edge contour information of the reconstructed image better, and achieve better reconstruction effect.