A water pumping system model has been designed based on the double-walled carbon nanotube. In this system, the inner tube is fixed as the water channel, while the exterior one can move, similar to the piston motion along the axial direction, to create a pumping force. Molecular dynamics simulations confirm that both the water flux and the water dipole orientation are sensitive to the velocity of motions of the outer tube so that a controllable unidirectional water flow can be achieved in this system by varying the velocity. Its pumping ability comes mainly from the carbon-water van der Waals driving forces of the exterior tube. The piston motion of the outer tube changes the position of the vdW balance point, which not only leads to the increase of vdW force on the water molecules already residing in the inner tube, but also enlarges their accelerated distance. Meanwhile, the orientation of water molecules inside the inner tube is strongly coupled to the water flux, the probability of +dipole states attains unity at v = 0.05 Å/ps, where the water flux reaches its maximum value (2.02 ns-1). Compared to the pump which is controlled by uniform electric field, the transmission efficiency of our mechanical pump is higher. This design may open a new way for water pumping in the field of nanodevices.