The goal is non-linear weighted type half-scan algorithm for reconstruction of a long object, which has important applications for clinical CT. Image reconstruction from cone-beam projections collected along a half-scan trajectory is commonly done using the Feldkamp-type half-scan algorithm, which performs well only with a large cone angle. Half-scan CT algorithms are advantageous in terms of temporal resolution, and widely used in fan-beam and cone-beam geometry. We propose a non-linear weight based algorithm to increase the cone angle by several folds to achieve satisfactory image quality at the same radiation dose. In our scheme, we first weighting with respect to half-scan projection data at individual projection angles is changed. Then, distribution of correction coefficients so that they are large near the center of the detector, while taking individual channel data for the detector into account, and smaller near the edges. Finally, three-dimensional back-projection of corrected half-scan projection data. Numerical phantoms are used to assess image quality indexes. Comparison with Feldkamp-type half-scan reconstruction is conducted. Numerical simulation studies are performed to verify the correctness and demonstrate performance. Image quality of the long object reconstruction is similar to that of the short object reconstruction. Our non-linear weighted half-scan reconstruction algorithms allow minimization of redundant data and optimization of temporal resolution, and outperform Feldkamp-type half-scan algorithm. These algorithms seem promising for quantitative and dynamic biomedical applications of cone-beam tomography. We extended our non-linear weighted half-scan method into a solution to the long object problem. Our non-linear weighted half-scan algorithm has a potential for CT in cone-beam geometry.