Abstract: The mechanism of controlling water wave by designing special variable-density fluid is studied through theoretical analysis and numerical simulation based on the principle of gradient refractive index optical lens.The impact of water waves on water-related projects can be alleviated by designing variable-density fluid lens to make parallel incident water waves turn back and propagate backwards according to the principle of the Eaton lens which could deflect ray trajectories,hence reducing wave intensity in downstream area.On the other hand,water wave energy can be better collected and exploited by designing variable-density fluid lens to make parallel incident water wave focus to a point and enhance wave intensity in light of the Luneburg lens which can focalize ray trajectories.Our study proves that it is feasible to regulate and control surface water waves by designing and arranging variable-density fluid regions of different sizes and functions according to specific application requirements and project conditions.The theory and technique in this paper provides a new idea for controlling and utilizing waves in water conservancy and ocean engineering.

Key words: water wave, gradient index lens, variable density fluid area, Luneburg lens, Eaton lens