A method for calibrating and reconstructing material density images in a dual-spectral computed tomography (CT) system 100 is disclosed. An X-ray source in the CT system 100 emits a first X-ray spectrum and a second X-ray spectrum towards an object. The method includes computing calibration coefficients by using projection data from the object for the two X-ray spectra and by linearizing at least two basis materials such as bone and water simultaneously. Further, basis materials decomposition coefficients for the at least two basis materials are computed by linearizing the basis materials individually. Correction values for the projection data and for the basis materials are then computed by using the basis materials decomposition coefficients and the calibration coefficients. The computed correction values are used in reconstructing material density images for the basis materials.