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Electrical impedance tomography (EIT) is a new kind of noninvasive computer imaging technique. The imaging process of EIT is known as inverse problem, and the back projection algorithm is widely used to solve this problem in practice. However, the image can only be reconstructed with low resolution and interfered by artifacts using this algorithm. This paper proposes a new filter back projection algorithm for improving the quality of the image. Being different with other existing algorithms, this algorithm uses RL (Ramachandran and Lakshminarayanan) filter function to get ride of image artifacts and interference. Because the RL filtering function will take obvious oscillations while image reconstructing, the means method is utilized to modify the filter function in this paper. The results of numerous simulation experiments show the new algorithm can obtain much better resolution and less artifacts compared with existing back projection algorithms and filter algorithms using RL filter function.