In this paper, we aim at a polychromatic physics model of dual-energy medical x-ray imaging and present a corresponding computation method, which includes two steps: first, bd(s, theta), i.e. the parameter used for expressing the component of Compton scatter, and bp(s, theta), i.e. the parameter used for expressing the component of Photoemission Effect, are decided by solving a nonlinear equation system; then a FBP ( Filtered Back Projection ) algorithm is used to reconstruct the decomposition images from the sinograms of bp(s, theta) and bp(s, theta). It is noticed that the first step is the most time-consuming, so it is very important to find out a high-speed and effective iteration computation method. In this paper, we propose a Newton iteration method with an effective estimation strategy of initial value for quickly solving the nonlinear equation system. A CT simulation experiment was implemented to validate the effectiveness of the whole procedure.