As one of the most commonly used natural languages, gesture has become an important approach for people to interact with machines. However, the flexibility of fingers has posed a challenge for detecting fine-grained gestures. In this paper, a novel method of high precision fine-grained gesture recognition is proposed based on a terahertz radar, which is able to sense any gesture movement when its range of motion is greater than 5mm. First, High Resolution Range Profile (HRRP) sequences are extracted from radar echoes. Then, the HRRP features are fed to Random Forest classifier after dimensionality reduction by PCA. In order to verify the proposed method is effective to detect fine-grained gestures, four kinds of similar gestures with multi-fingers are designed for experiments. The results indicate the recognition rate exceeds 99.7%, which demonstrates a great prospect in fine-grained gesture recognition using a terahertz radar.