In the medical imaging field, iterative methods have become a hot topic of research due to their capacity to resolve the reconstruction problem from a limited number of projections. This gives a good possibility to reduce radiation exposure on patients during the data acquisition. However, due to the complexity of the data, the reconstruction process is still time consuming, especially for 3D cases, even though implemented on modern computer architecture. Time of the reconstruction and high radiation dose imposed on patients are two major drawbacks in computed tomography. With the aim to resolve them effectively, we adapted Least Square QR method with soft threshold filtering technique for few-view image reconstruction and present its numerical validation. The method is implemented using CUDA programming mode and compared to standard SART algorithm. The numerical simulations and qualitative analysis of the reconstructed images show the reliability of the presented method.