—Laser surgery requires accurate following of a path defined by the surgeon, while the velocity on this path is dependent on the laser-tissue interaction. Therefore, path following and velocity profile control must be decoupled. In this paper, non-holonomic control of the unicycle model is used to implement velocity-independent visual path following for laser surgery. The proposed controller was tested, in simulation as well as experimentally in several conditions of use: different initial velocities (step input, successive step inputs, sinusoidal inputs), optimized/non-optimized gains, time-varying path (simulating a patient breathing), and complex curves with curvatures. Thereby, experiments at 587 Hz (frames/second) show an average accuracy lower than 0.22 pixels (≈ 10µm) with a standard deviation of 0.55 pixels (≈ 25µm) path following, and a relative velocity distortion of less than 10 −6 %.