Acoustic wave resonators are promising candidates for gravimetric biosensing. However, they generally suffer from strong acoustic radiation in liquid, which limits their quality factor and increases their frequency noise. This article presents an acoustic radiation-free gravimetric biosensor based on a locally resonant surface phononic crystal (SPC) consisting of periodic high aspect ratio electrodes to address the above issue. The acoustic wave generated in the SPC is slower than the sound wave in water, hence it prevents acoustic propagation in the fluid and results in energy confinement near the electrode surface. This energy confinement results in a significant quality factor improvement and reduces frequency noise. The proposed SPC resonator is numerically studied by finite element analysis and experimentally implemented by an electroplating-based fabrication process. Experimental results show that the SPC resonator exhibits an in-liquid quality factor 15 times higher than a conventional Rayleigh wave resonator at a similar operating frequency. The proposed radiation suppression method using SPC can also be applied in other types of acoustic wave resonators. Thus, this method can serve as a general technique for boosting the in-liquid quality factor and sensing performance of many acoustic biosensors.