The COVID-19 pandemic has prompted technological measures to control the spread of the disease. Private contact tracing (PCT) is one of the promising techniques for the purpose. However, the recently proposed Bluetooth-based PCT has several limitations in terms of functionality and flexibility. The existing systems are only able to detect direct contact (i.e., human-human contact), but cannot detect indirect contact (i.e., human-object, such as the disease transmission through surface). Moreover, the rule of risky contact cannot be flexibly changed with the environmental situation and the nature of the virus. In this paper, we propose a secure and efficient trajectory-based PCT system using trusted hardware. We formalize trajectory-based PCT as a generalization of the well-studied Private Set Intersection (PSI), which is mostly based on cryptographic primitives and thus insufficient. We solve the problem by leveraging trusted hardware such as Intel SGX and designing a novel algorithm to achieve a secure, efficient and flexible PCT system. Our experiments on real-world data show that the proposed system can achieve high performance and scalability. Specifically, our system (one single machine with Intel SGX) can process thousands of queries on 100 million records of trajectory data in a few seconds.