Sensitivity encoding （SENSE） is a widely used parallel magnetic resonance imaging （MRI） reconstruction model. Many improved models have been proposed to improve the reconstruction performance of SENSE. However， the reconstructed images of these improved methods still have many artifacts. Especially， it is difficult to reconstruct a clearer image when the acceleration factor is higher. Therefore， based on nonlocal low-rank（NLR） constraints， this paper proposes an improved SENSE model， named NLR-SENSE model， which can effectively improve the quality of parallel MRI reconstructed images. We adopt the weighted kernel norm as the rank surrogate function， and use the alternating direction multiplier method （ADMM） to solve the NLR-SENSE model. Simulation results show that， compared with several other parallel MRI reconstruction methods， the NLR-SENSE model performs better in visual comparison and three different objective metrics， and can effectively improve the quality of the reconstructed image.