Dual-energy CT can be represented as the dual-energy equations by decomposing the linear attenuation coefficient of the X-ray scanned object into two material basis functions of photoelectric absorption and Compton scatter. To solve the dual-energy equations, in this paper, we apply the mean-value theorem for integrals and propose a new projection-based iterative algorithm. We discuss the convergence of the proposed algorithm and carry out various numerical simulations for demonstrating its feasibility.