Removing non-brain tissues such as the skull, scalp and face from head computed tomography (CT) images is an important field of study in brain image processing applications. It is a prerequisite step in numerous quantitative imaging analyses of neurological diseases as it improves the computational speed and accuracy of quantitative analyses and image coregistration. In this study, we present an accurate method based on fully convolutional neural networks (fCNN) to remove non-brain tissues from head CT images in a time-efficient manner. The method includes an encoding part which has sequential convolutional filters that produce activation maps of the input image in low dimensional space; and it has a decoding part consisting of convolutional filters that reconstruct the input image from the reduced representation. We trained the fCNN on 122 volumetric head CT images and tested on 22 unseen volumetric CT head images based on an expert's manual brain segmentation masks. The performance of our method on the test set is: Dice Coefficient= 0.998±0.001 (mean ± standard deviation), recall=0.998±0.001, precision=0.998±0.001, and accuracy=0.9995±0.0001. Our method extracts complete volumetric brain from head CT images in 2s which is much faster than previous methods. To the best of our knowledge, this is the first study using fCNN to perform skull stripping from CT images. Our approach based on fCNN provides accurate extraction of brain tissue from head CT images in a time-efficient manner.