Computed tomography (CT) has great impact in many fields such as medical applications, industrial inspection, etc... Low dose constraints and Limited projection are common problems in a variety of tomographic reconstruction examples which lead to wrong data. In this work, we propose a method of CT reconstruction based on the simultaneous iterative reconstruction techniques SIRT improved by imposing positivity constraint in the total variation (TVcim-p). We test our method with on Shepp-Logan phantom and different reconstruction methods. The results show that the proposed algorithm can gives images with quality comparable to other algorithms.