Achieving a fast, unidirectional flow of single-file water molecules (UFSWM) across nanochannels is important for membrane-based water purification or seawater desalination. For this purpose, electro-osmosis methods are recognized as a very promising approach and have been extensively discussed in the literature. Utilizing molecular dynamics simulations, here we propose a design for pumping water molecules in a single-walled carbon nanotube in the presence of a linearly gradient electric (GE) field. Such a GE field is inspired by GE fields generated from charged ions located adjacent to biological membrane water nanochannels that can conduct water in and out of cells and can be experimentally achieved by using the charged tip of an atomic force microscope. As a result, the maximum speed of the UFSWM can be 1 or 2 orders of magnitude larger than that in a uniform electric (UE) field. Also, inverse transportation of water molecules does not exist in case of the GE field but can appear for the UE field. Thus, the GE field yields a much more efficient UFSWM than the UE field. The giant pumping ability as revealed is attributed to the nonzero net electrostatic force acting on each water molecule confined in the nanotube. These observations have significance for the design of nanoscale devices for readily achieving controllable UFSWM at high speed.