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This study introduces the first shear-horizontal surface acoustic wave (SH-SAW) resonator with multiple modes based on a thin film lithium niobate on insulator (LNOI) platform. To confine acoustic energy and reduce internal reflections, we have evenly distributed metal gratings across the resonant cavity with a period half the electrode pitch serve as a surface waveguide. While the frequency range of the multimode resonance is limited by the fractional bandwidth (FBW R ) of the phononic bandgap of the Bragg reflectors, we have achieved a broad bandgap with an FBW R of 18.3% in this work through the use of gold (Au) metal strips on the LNOI substrate. In our prototype design, we have observed five SH-SAW resonances that are equally-spaced across the frequency range of 536.7 to 620 MHz, with an interval of approximately 21 MHz. These resonances exhibit high quality factors (Q > 300, Q max = 476) and large electromechanical coupling coefficients \left( {k_{{\text{eff}}}^2 > 1.27\% ,k_{{\text{eff}},\max }^2 = 3.67\% } \right), accompanied by clear phase transitions, demonstrating significant potential for applications in RF signal processing.