Water confined in carbon nanotube channels exhibits structures and dynamics different from bulk water. When the diameter of carbon nanotubes is reduced to about 0.8 nm， water molecules arranges themselves into a single-file chain similar to that in biological water channels， which shows extremely high flow rates and ion repulsion capabilities. Empirical potential-based molecular dynamics simulations have been widely used to reveal the structures and dynamic properties of the single-file water. However， the selected water models and interaction parameters between water and wall atoms significantly affect the simulation results. In this work， a deep-learning potential is developed for the single-file water chain by training deep neural networks based on datasets obtained from ab initio molecular dynamics. Molecular dynamics simulations using the deep learning potential can reproduce the potential energy and atomic force with the accuracy near the first-principle calculations but at much lower computational costs. They can also reproduce the properties of the single-file water obtained in ab initio molecular dynamics， including the distributions of O-H bond length， H-O-H bond angle， orientation angle and density. In addition， we compare the results from deep learning potentials based simulations with those based on traditional water models. The developed deep learning potential enables simulations of single-file water systems with large system sizes and time scales， at the accuracy near the first-principle calculations.