A new reconstruction method, which is called Generalized Vector Sampled Pattern Matching (GVSPM) method, has been applied to an ill-posed inverse problem of a capacitance-computed tomography for solid air two-phase flow. In pseudo two-phase flow images, the correlation of the reconstructed images by GVSPM is higher than those by a conventional Newton Raphson (NR) iterative method by 32.5%. Moreover, in solid air two-phase flow images, the deviation between the particles volume fraction by experimental capacitance and that by the reconstruction methods is calculated. As a result, the volume fraction deviation of GVSPM reconstructed image is lower than that of NR by 56.7%. Also, the time-mean correlation between the experimental capacitance and the capacitances from the reconstruction method is calculated. As a result, GVSPM method improves the correlation by 23.6% as compared with NR method. The accurate reconstruction of GVSPM results from an inner product calculation between the experimental capacitance and the capacitance from the reconstructed images as an objective function.