The 80% of the matter in the Universe is in the form of dark matter that comprises the skeleton of the large-scale structure called the Cosmic Web. As the Cosmic Web dictates the motion of all matter in galaxies and inter-galactic media through gravity, knowing the distribution of dark matter is essential for studying the large-scale structure. However, the Cosmic Web's detailed structure is unknown because it is dominated by dark matter and warm-hot inter-galactic media, both of which are hard to trace. Here we show that we can reconstruct the Cosmic Web from the galaxy distribution using the convolutional-neural-network-based deep-learning algorithm. We find the mapping between the position and velocity of galaxies and the Cosmic Web using the results of the state-of-the-art cosmological galaxy simulations, Illustris-TNG. We confirm the mapping by applying it to the EAGLE simulation. Finally, using the local galaxy sample from Cosmicflows-3, we find the dark-matter map in the local Universe. We anticipate that the local dark-matter map will illuminate the studies of the nature of dark matter and the formation and evolution of the Local Group. High-resolution simulations and precise distance measurements to local galaxies will improve the accuracy of the dark-matter map.