Frequency generators and sensors increasingly require quartz resonators vibrating in high-frequency with high Q-factor. Currently, most of high-frequency resonators vibrating in above 150 MHz are overtone mode type, which is not so easy to achieve high Q-factor comparing with fundamental-type resonators. Since the quartz etching process technology has been improved, it becomes possible to fabricate thin plate of quartz resonator to achieve a high frequency value of fundamental mode. The fundamental mode resonators are gradually applied. To achieve a high Q-factor value, the dimension should be optimized to restrain vibration energy under the electrodes of resonators. Many efficient achievements have been acquired in this research field. However, many works focus on electrode dimension, and do not describe much for support part. In this work, we applied energy trapping analysis to optimizing support structure for a fundamental type quartz resonator with high frequency value. A new structure with symmetric support parts was designed and optimal dimensions were presented.