In this paper, a theoretical model for depicting shear horizontal wave (SH) propagation in a periodic plate with stubs is established, based on which the band structures are obtained numerically. Then, accuracy of this model is validated via compassion with the results from finite element method. After that, the influence of stub height on the fundamental mode of SH wave (SH0) is systematically investigated, and results indicate that the phase velocity of SH0 wave decreases with increasing of stub height. With aid of sensitivity of phase velocity to the stub height, an SH0wavebased lens for focusing plane wave is designed, and its working performance is examined, including the focusing position, energy distribution, and frequency bandwidth. It is revealed that the lens designed has a good performance, with an accurate focusing position and an evident focusing phenomenon. Additionally, the lens exhibits broadband, which can work in a certain frequency range that centered around the designed frequency. The design scheme in this paper provide a new idea for applications of energy harvesting, ultrasonic medicine, nondestructive testing, noise reduction and so forth.