Blockchain is becoming popular as a distributed and reliable ledger which allows distrustful parties to transact safely without trusting third parties. Emerging blockchain systems like Ethereum support smart contracts where miners can run arbitrary user-defined programs. However, one of the biggest concerns about the blockchain and the smart contract is privacy, since all the transactions on the chain are exposed to the public. In this paper, we present ShadowEth, a system that leverages hardware enclave to ensure the confidentiality of smart contracts while keeping the integrity and availability based on existing public blockchains like Ethereum. ShadowEth establishes a confidential and secure platform protected by trusted execution environment (TEE) off the public blockchain for the execution and storage of private contracts. It only puts the process of verification on the blockchain. We provide a design of our system including a protocol of the cryptographic communication and verification and show the applicability and feasibility of ShadowEth by various case studies. We implement a prototype using the Intel SGX on the Ethereum network and analyze the security and availability of the system.