An approximate image reconstruction method for gantry tilted multi slice computed tomography (MSCT) is presented in this paper, which extends the Feldkamp cone beam reconstruction algorithm to overcome its inaccuracy problem caused by large cone angle. This is done by tilting the reconstructing planes to minimize the cone angle and optimally fitting the spiral segment of the source. It is shown that the image reconstruction performance of the proposed algorithm is superior to that of the Feldkamp reconstruction algorithm. Because a 3D projection data set is employed, the proposed algorithm can use the projection more efficiently than 2D approximate reconstruction algorithms. With the reduced distance from the X-ray source to the reconstruction plane, the maximum pitch value of the proposed algorithm is larger than that of conventional Feldkamp algorithm. The proposed algorithm can archive higher volume coverage speed than Feldkamp algorithm.