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Cyber threat hunting is a proactive search process for hidden threats in the organization's information system. It is a crucial component of active defense against advanced persistent threats (APTs). However, most of the current threat hunting methods rely on Cyber Threat Intelligence(CTI), which can find known attacks but cannot find unknown attacks that have not been disclosed by CTI. In this paper, we propose LogKernel, a threat hunting method based on graph kernel clustering which can effectively separates attack behaviour from benign activities. LogKernel first abstracts system audit logs into Behaviour Provenance Graphs (BPGs), and then clusters graphs by embedding them into a continuous space using a graph kernel. In particular, we design a new graph kernel clustering method based on the characteristics of BPGs, which can capture structure information and rich label information of the BPGs. To reduce false positives, LogKernel further quantifies the threat of abnormal behaviour. We evaluate LogKernel on the malicious dataset which includes seven simulated attack scenarios and the DAPRA CADETS dataset which includes four attack scenarios. The result shows that LogKernel can hunt all attack scenarios among them, and compared to the state-of-the-art methods, it can find unknown attacks.