Global warming caused by greenhouse gas emissions has become a worldwide environmental problem, posing a great threat to human survival. As the world’s largest emitter of carbon dioxide, China has pledged to reach peak carbon emissions by no later than 2030 and carbon neutrality by 2060. It is found that a carbon tax is a powerful incentive to reduce carbon emissions and promote an energy revolution, but it may have negative socio-economic impacts. Therefore, based on China’s 2020 input–output table, this paper systematically investigates the impacts of a carbon tax on China’s economy, carbon emissions, and energy by applying a computable general equilibrium model to determine the ideal equilibrium between socio-economic and environmental objectives. Based on energy use characteristics, we subdivided the energy sector into five major sectors: coal, oil, natural gas, thermal power generation, and clean power. The results show that when the carbon emission reduction target is less than 15%, that is, when the equilibrium carbon tax price is less than 54 yuan/ton, the implementation of a carbon tax policy can significantly reduce carbon emission and fossil fuel energy consumption, while only slightly reducing economic growth rate, and can achieve the double dividend of environment and economy. Moreover, because the reduction of coal consumption has the greatest impact on reducing carbon emissions, the ad valorem tax rate on coal after the carbon tax is imposed is the highest because coal has the highest carbon emission coefficient among fossil fuels. In addition, as an emerging clean energy source, hydrogen energy is the ideal energy storage medium for achieving clean power generation in power systems. If hydrogen energy can be vigorously developed, it is expected to greatly accelerate the deep decarbonization of power, industry, transportation, construction, and other fields.