Deep learning methods have shown great success in pixel-wise prediction tasks. One of the most popular methods employs an encoder-decoder network in which deconvolutional layers are used for up-sampling feature maps. However, a key limitation of the deconvolutional layer is that it suffers from the checkerboard artifact problem, which harms the prediction accuracy. This is caused by the independency among adjacent pixels on the output feature maps. Previous work only solved the checkerboard artifact issue of deconvolutional layers in the 2D space. Since the number of intermediate feature maps needed to generate a deconvolutional layer grows exponentially with dimensionality, it is more challenging to solve this issue in higher dimensions. In this work, we propose the voxel deconvolutional layer (VoxelDCL) to solve the checkerboard artifact problem of deconvolutional layers in 3D space. We also provide an efficient approach to implement VoxelDCL. To demonstrate the effectiveness of VoxelDCL, we build four variations of voxel deconvolutional networks (VoxelDCN) based on the U-Net architecture with VoxelDCL. We apply our networks to address volumetric brain images labeling tasks using the ADNI and Loni LPBA40 datasets. The experimental results show that the proposed iVoxelDCNa achieves improved performance in all experiments. It reaches 83.34% in terms of dice ratio on the ADNI dataset and 79.12% on the Loni LPBA40 dataset, which increases 1.39% and 2.21% respectively compared with the baseline. In addition, all the variations of VoxelDCN we proposed outperform the baseline methods on the above datasets, which demonstrates the effectiveness of our methods.