Dual-energy computed tomography (CT) is to reconstruct images of an object from two projection datasets generated from two distinct x-ray source energy spectra. It can provide more accurate attenuation quantification than conventional CT with a single x-ray energy spectrum. In the diagnostic energy range, x-ray energy-dependent attenuation can be approximated as a linear combination of photoelectric absorption and Compton scattering. Hence, two physical components of x-ray attenuation can be determined from two spectrally informative projection datasets to achieve monochromatic imaging and material decomposition. In this paper, a projection-domain image reconstruction method is proposed to accurately quantify the two attenuation components for dual-energy CT. This method combines both an analytical algorithm and a single-variable optimization method to solve the non-linear polychromatic x-ray integral model, allowing an efficient and accurate decomposition of physical basis components. Numerical tests are performed to illustrate the merit of the proposed method.