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Interest exists in the development and applications of new CT systems that can collect multiple sets of data, including energy-integrating and/or photon-counting data. Practical utilities of such systems include improving image quality and, more importantly, exploiting spectral information for enabling imaging systems and configurations of clinical significance. In the work, instead of using data-based decomposition combined with standard analytic-based reconstruction, we propose an optimization-based reconstruction method for CT systems with multiple data sets. The method consists of a linearized data model, optimization program, and associated algorithm specifically designed for images resulting from data collected in such CT systems. Simulation studies using two distinct diagnostic range kV spectra show the robustness and effectiveness of the proposed method in correcting for non-linear beam hardening artifacts in CT images.