This paper focuses on designing a structure using a laser ultrasound technique, wherein wedge waves can propagate without dispersion. First, the impact of curvature radius and truncations on the wedge waves are investigated using finite element method, and the dispersion curves are obtained using a two-dimensional Fourier transformation method. Subsequently, the propagation of non-dispersive wedge waves is realized via a special wedge shape, which was designed with a unique relationship between the curvature radius and truncation, and its correctness is validated using numerical simulation. Finally, experiments are performed to detect the wedge waves, wherein a pulsed laser is coupled with optical fiber excitation, and the waves are detected using an optical vibrometer.