The last decade has witnessed unprecedented de-velopment in blockchain smart contracts. While smart contracts inherit the decentralization and other security properties of blockchain, they are hampered by the lack of privacy protection and poor performance of blockchain. In this paper, we propose a parallel contract execution framework, ParaEthereum, that combines blockchain and trusted execution environments (TEEs) to construct private, efficient, and scalable smart contracts. By introducing TEEs, ParaEthereum performs contract execution off the chain through enclave-enabled computing nodes and confirms the correctness of the execution results on the chain, achieving the decoupling of contract execution and consensus. To meet system availability requirements and enable concurrent exe-cution of transactions, each transaction is executed independently by a set of computing nodes determined by its execution set, and different computing nodes process transactions within the block concurrently based on the constructed transaction dependency graph. We also conducted extensive tests on our proposed scheme with respect to its efficiency and effectiveness.