This study uses game-theory to construct a dual-channel green supply chain consisting of a manufacturer, a blockchain-enabled platform, and a non-blockchain-enabled offline retailer, with the aim of comparing two government subsidy strategies: greenness investment cost subsidy and production subsidy, and exploring the impact of blockchain adoption. First, firms without government subsidy should adopt blockchain only when privacy costs are low. Both subsidy strategies can always motivate the manufacturer to increase greenness investment levels and achieve a triple-win situation. Second, when the government controls the greenness investment level, the demand, profits, and subsidy amount under cost subsidy are always lower than those under production subsidy. Third, when the government controls the subsidy amount, the greenness investment level under cost subsidy is always higher than that under production subsidy. The offline demand and retailer’s profit are higher under production subsidy, while the online demand and platform’s profit are higher under cost subsidy. The manufacturer’s profit is higher under cost subsidy only when the subsidy level is low. Additionally, regardless of governmental goals, the platform’s profit is always higher than the retailer’s profit, indicating that downstream firms under government subsidy should always adopt blockchain.