We propose an optical tweezer with tunable potential wells, by dynamically manipulating the phase gradient of light. Using our proposed method to design holograms, we can obtain desirable phase profiles and intensity distributions of optical traps. Optical force arising from phase gradient creates tunable potential wells for versatile optical nanomanipulation, such as trapping nanoparticles in peanut-shaped optical spots, positioning and shifting nanoparticles in optical gears, and controllable transport, as demonstrated in our experiments. The tunable optical tweezer has several merits including flexible design, easy control and high tunability, which provides a new tool for exploring novel functions in optical nanomanipulation.