Non-linear partial volume effect is still an unsolved problem in the theory and application of computed tomography reconstruction. In this work， an optimization-based reconstruction algorithm for effectively solving this effect was studied and developed. The discrete non-linear X-ray projection transformation model was established， when the inverse problem of X-ray projection transformation was transformed into a non-convex optimization. A non-linear iterative reconstruction algorithm was formulated to solve the non-convex optimization problem by tailoring the first-order primal-dual algorithm developed originally for solving convex optimization problems. Using computer-simulation studies， the convergence and reconstruction accuracy of the algorithm was demonstrated in this investigation. Images reconstructed were examined first through visual inspection with extremely narrow display window for revealing a contrast level of less than 1%， and then assessed with quantitative metrics such as the normalized l₂-norm of the difference relative to its truth images. The simulation results show that the non-linear reconstruction algorithm can converge to the real image within the range of calculation accuracy， and the reconstructed image can also be displayed for the details with image contrast less than 1%. This would provide a reference for the design of computed tomography imaging application algorithm which can effectively compensate the non-linear partial volume effect artifacts.