We propose an emission-intensity-based carbon-tax policy for the electric-power industry and investigate the impact of the policy on thermal generation self-scheduling in a deregulated electricity market. The carbon-tax policy is designed to take a variable tax rate that increases stepwise with the increase of generation emission intensity. By introducing a step function to express the variable tax rate, we formulate the generation self-scheduling problem under the proposed carbon-tax policy as a mixed integer nonlinear programming model. The objective function is to maximize total generation profits, which are determined by generation revenue and the levied carbon tax over the scheduling horizon. To solve the problem, a decomposition algorithm is developed where the variable tax rate is transformed into a pure integer linear formulation and the resulting problem is decomposed into multiple generation self-scheduling problems with a constant tax rate and emission-intensity constraints. Numerical results demonstrate that the proposed decomposition algorithm can solve the considered problem in a reasonable time and indicate that the proposed carbon-tax policy can enhance the incentive for generation companies to invest in low-carbon generation capacity.