Smart contracts are programs running on the blockchain. Comments in source code provide meaningful information for developers to facilitate code writing and understanding. Given various kinds of token standards in smart contracts (e.g., ERC-20, ERC-721), developers often copy&paste code from other projects as templates, and then implement their own logic as add-ons to such templates. In many cases, the consistency between code and comment is not well-aligned, leading to comment-code inconsistencies (as we call CCIs). Such inconsistencies can mislead developers and users, and even introduce vulnerabilities to the contracts. In this paper, we present SmartCoCo, a novel framework to detect comment-code inconsistencies in smart contracts. In particular, our research focuses on comments related to roles, parameters, and events that may lead to security implications. To achieve this, SmartCoCo takes the original smart contract source code as input and automatically analyzes the comment and code to find potential inconsistencies. SmartCoCo associates comment constraints and code facts via a set of propagation and binding strategies, allowing it to effectively discover inconsistencies with more contextual information. We evaluated SmartCoCo on 101,780 unique smart contracts on Ethereum. The evaluation result shows that SmartCoCo achieves good effectiveness and efficiency. In particular, SmartCoCo reports 4,732 inconsistencies from 1,745 smart contracts, with a precision of over 79% on 439 manual-labeled comment-code inconsistencies. Meanwhile, it only takes 2.64 seconds to check a smart contract on average.