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Since the tax of carbon emission is popular and consumers are exhibiting low-carbon preference, the green manufactures have to spend more extra cost on investing carbon emission reduction (CER) technology to decrease the carbon emission. To encourage the manufacture's CER investment efforts, this paper explores the impact of carbon tax, CER cost, and consumers' low-carbon preference on low-carbon decision-making and designs a revenue-sharing contract (RS) by constructing Stackelberg models. Based on the theoretical and numerical analysis, this paper finds that the supply chain would benefit from the increment of consumer's environmental awareness but be depressed by the increase of the CER investment cost factor. Additionally, there exists a unique optimal carbon tax to make CER degree the maximum. Furthermore, RS can effectively promote manufacturers to reduce carbon emissions and also improve the supply chain efficiency. [ABSTRACT FROM AUTHOR]