Due to the high similarity of gray values among liver and adjacent organs in Computed Tomography （CT） and Magnetic Resonance Imaging （MRI） images， a 3D liver image segmentation method based on multi-scale feature fusion and grid attention mechanism， namely MAGNet （Multi-scale feature fusion And Grid attention mechanism Network）， was proposed to segment liver automatically and accurately. Firstly， high-level features and low-level features were connected by the attention-guided concatenation module to extract important context information， and the grid attention mechanism was introduced in the attention-guided concatenation module to focus on the segmentation region of interest. Then， the multi-scale feature fusion module was formed by the layered connection in a single feature map according to the number of channels， and this module was used to replace the basic convolutional block to obtain multi-scale semantic information. Finally， the deep supervision mechanism was utilized to solve the problems of vanishing gradient， exploding gradient and slow convergence. Experimental results show that on 3DIRCADb dataset， compared with the U³-Net+DC method， MAGNet improves the Dice Similarity Coefficient （DSC） metric by 0.10 percentage points and reduces the Relative Volume Difference （RVD） metric by 1.97 percentage points； on Sliver07 dataset， compared with the CANet method， MAGNet improves the DSC metrics by 0.30 percentage points， reduces Volumetric Overlap Error （VOE） metrics by 0.68 percentage points， and reduces the Average Symmetric Surface Distance （ASD） and Root Mean Square Symmetric Surface Distance （RMSD） metrics 0.03 mm and 0.22 mm respectively； on the liver MRI dataset of a hospital， MAGNet also has good results on all metrics. Besides， MAGNet was applied to a mixed dataset of 3DIRCADb dataset and the hospital liver MRI dataset above， and a competitive segmentation result was also achieved.