Quantitative imaging based on dual energy computed tomography (DECT) is useful in both medical and industrial areas. However, the dependence of the attenuation coefficient on X-ray energy and the polychromatic property of X-ray beams bring obstacles for dual energy image reconstruction. In this paper, attenuation coefficient function μ(E) is approximated with the basis material model. And X-ray spectra which govern the projection functions are estimated from transmission measurements. With these two foundations, we obtain a practical reconstruction method for DECT. The distribution of effective atomic number, electron density, and linear attenuation coefficient at any desirable energy can be reconstructed using the proposed method. Numerical simulations and practical experiments were conducted to evaluate the accuracy and practicability of the method.