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Recently, Decentralized Finance (DeFi) platforms on Ethereum are booming, and numerous traders are trying to capitalize on the opportunity for maximizing their benefits by launching front-running attacks and extracting Miner Extractable Values (MEVs) based on information in the public mempool. To protect end users from being harmed and hide transactions from the mempool, private transactions, a special type of transactions that are sent directly to miners, were invented. Private transactions have a high probability of being packed to the front positions of a block and being added to the blockchain by the target miner, without going through the public mempool, thus reducing the risk of being attacked by malicious entities. Despite the good intention of inventing private transactions, due to their stealthy nature, private transactions have also been used by attackers to launch attacks, which has a negative impact on the Ethereum ecosystem. However, existing works only touch upon private transactions as by-products when studying MEV, while a systematic study on private transactions is still missing. To fill this gap and paint a complete picture of private transactions, we take the first step towards investigating the private transactions on Ethereum. In particular, we collect large-scale private transaction datasets and perform analysis on their characteristics, transaction costs and miner profits, as well as security impacts. This work provides deep insights on different aspects of private transactions.