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In recent years, more attention has been paid to water surface environment protection. Current water surface waste cleaning mainly relies on manual operations, which are low-efficiency and dangerous. Therefore, in this paper, we design a fully autonomous water surface cleaning robot, SMURF, which achieves high-efficiency water surface cleaning without human operation and adapts to be used in various types of real-world water bodies. In addition, we propose a novel coverage path planning method on water surfaces and an improved nonlinear model predictive controller. The real-world experiment shows that SMURF works well in different kinds of water bodies and achieves much higher efficiency than traditional water surface cleaning methods.