Climate regulations tend to target energy-intensive sectors whose products are widely used in industrial production as intermediate inputs, and carbon abatement may be partially offset by intermediate input-led leakage. This paper aims to examine the impact of intermediate input linkages on carbon leakage both theoretically and empirically. The theoretical part develops a Harberger-type model with an input-output linkage structure, identifies four leakage effects and derives closed-form solutions for these leakage effects. Its empirical part builds a computable general equilibrium model of China's economy and introduces structural decomposition analysis to link the theoretical and empirical models. When imposing a carbon price on the electricity generation sector, our results show significant sectoral carbon leakage. Our decomposition analysis further suggests that such leakage is mainly through the production substitution effect and the multiplier effect. Our results highlight the importance of sectoral linkage when discussing the carbon leakage issue of climate policies.