In this paper, we develop a new algorithm that enables the reconstruction of a region of interest (ROI) in X-ray Computed Tomography (CT), in case only a local region of the object is to be imaged. The method uses a Gaussian window function in order to reduce the X-ray attenuation from the region outside the ROI. The method uses almost completely local data and reduces the amount of exposure significantly. Many algorithms can be easily combined with our algorithm in order to improve the reconstruction quality. The main goal of this work is to reduce the bias in order to allow quantitative analysis of the CT-images.