The inception of blockchain techniques has been revolutionizing various domains, e.g., Internet of Things, supply chain and healthcare. Ethereum smart contracts emerge as the promising blockchain application, which could enable distrustful parties to participate in the automatic and trustful transactions. Given the increasing importance of Ethereum smart contracts, understanding them becomes imperative. However, prior work only studied smart contracts with general high-level patterns, and one critical question has not been answered yet: how do smart contracts behave individually? In this paper, we present a behavior-aware profiling of individual smart contract from a multi-party perspective, which improves the visibility of the smart contract ecosystem. We conduct a detailed study of the behavior of individual smart contract on two real-world datasets, and our profiling reveals interesting and surprising observations. For example, a few contract completion chains have more than 50 contracts and all of them belong to the Finance category. We also discuss the implications that lead to recommendations to improve the security and performance of the smart contract ecosystem. Overall, our work effectively complements previous work towards generating a comprehensive understanding of smart contracts.