Abstract: This paper investigated the focusing phenomena of Surface Acoustic Wave (SAW) field generated by a circular-arc Inter-Digital Transducer (IDT) on a piezoelectric crystal. A rigorous vector field theory of surface excitation on the crystal developed by the authors was used to evaluate the convergent SAW field instead of the prevalent scalar angular spectrum one used in optics. The theoretical results show that the anisotropy of a medium has great impact on the focusing properties of the acoustic beams, such as focal length and symmetrical distributions near the focus. A dark field method was used in experiment to observe the focusing of SAW field optically. Although the convergent phenomena of SAW field on the anisotropic media or piezoelectric crystals are very complicated, the experimental results were in agreement with those from the rigorous theory.