Automated and precise pneumonia segmentation of COVID-19 extends the view of medical supply chains and offers crucial medical supplies to fight the COVID-19 pandemic. Deep learning plays a vital role in improving the COVID-19 segmentation from computed tomography (CT) scans. However, the literature lacks a precise segmentation approach on small-size lesions because they often split the CT scan into 2-D slices or 3-D patches, leading to the loss of contextual and/or global information. In order to address this, this article proposes a novel fully volumetric segmentation network, called FV-Seg-Net, that effectively exploits the local and global spatial information and enables the entire CT volume processing at once. The decoder is designed using a computationally efficient recalibrated anisotropic convolution module that can acquire the 3-D semantic representation of the CT volumes with anisotropic resolution. To avoid losing information during down-sampling, we reconstruct the skip-connection using a multilevel multiscale pyramid aggregation module and ensure more effective context fusion that improves the reconstruction capability of the decoder. Finally, stacked data augmentation (StackAug) is presented to magnify the training data and improve the generalizability of FV-Seg-Net. Proof of concept experiments on two public datasets demonstrates that the FV-Seg-Net achieves excellent segmentation performance (Dice score: 85.69 and a surface-dice: 84.79%), outperforming the current cutting-edge studies.