An annular array transducer that generates omnidirectional shear-horizontal (SH) waves can be useful in plate inspection. This is because it quickly covers a wide inspection area and generates SH waves that propagate without much energy leakage in spite of various loading conditions in plates. If the transducer is installed on thick plates, multiple modes of SH waves can be simultaneously generated, and their interference can result in poor inspection. Here, we propose new design method of the SH wave transducer to selectively generate the target single mode with high S/N ratios. Furthermore, we aim to generate SH waves that are omnidirectional because omnidirectional waves are preferred for efficient imaging. Our design method is to tailor the dimension and position of the transducer excitation elements based on the analytically calculated SH wave fields. We conducted a series of experiments as well as numerical simulations and confirmed that the proposed transducer performs as well as predicted by our analysis.