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Developing self-powered accelerometers with high sensitivity is vital for Internet of Things, wearable electronics and sensor networks. Triboelectric nanogenerators (TENGs) have been proved as an effective solution for self-powered sensing. Currently, the research on self-powered accelerometers based on TENG still lacks the applicable theoretical model. And most self-powered accelerometers also have relatively low sensitivity. In this work, a novel V-Q-atheoretical model is reported to develop a self-powered and high sensitivity acceleration sensor based on TENGs. Deduced by the established model, the output performance of the sensor can be derived from theoretical calculations. Guided by the calculations, an accelerometer based on the silk-fibroin TENG is fabricated. The sensor exhibits a high sensitivity of 20.4 V/(m/s2) when acceleration ranges from 1 to 11 m/s2, and a high-power density of 371.8 mW/m2. These experimental results show a good agreement with the theoretical analysis. The development of the sensor shows many application prospects including wearable alarming devices and vibration detection systems. This research provides an in-depth theoretical study on self-powered acceleration sensors based on TENGs and an efficient method to develop high sensitivity self-powered acceleration sensors, which will promote the application of TENGs in self-powered sensing.