In the process of producing materials, the surface roughness always exists. And it can change the velocity of surface acoustic wave (SAW) which propagates in the material. To assess the properties of materials by laser induced SAW, an inverse method based on the wide-band velocity dispersion characteristic of laser-induced SAW is most commonly used. To study whether the surface roughness can be one of the inversion characteristic parameters, an experimental apparatus is constructed in this article. In the apparatus, the SAW is induced in the surface roughness sample by laser, and it is received by a polyvinylidene fluoride transducer with wide frequency band. Using this apparatus, we study the influences of different surface roughnesses on SAW velocity. In the paper a physical model of laser-induced SAW propagating in roughness surface is established theoretically. The time domain characteristic of SAW is obtained by the finite element method, and then the velocity dispersion curve of SAW is achieved. It is concluded that the theoretical result and the experimental result are in good agreement with each other. The studies in this article form theoretical and experimental bases for assessing surface roughness by means of laser-induced SAW technique.