Over the past two years, we have developed a series of algorithms for Grangeat-type half-scan based reconstruction of a short object. These algorithms allow high temporal resolution and high temporal consistence, and suppress Feldkamp-type reconstruction related artifacts. Therefore, this scheme is promising for dynamic and/or quantitative imaging. In this paper, we extend our work into a solution to the long object problem. Our approach takes a temporally non-optimized pre-reconstruction step to transform the long object problem into a short object problem. The detector area is analytically classified into desirable, corrupted, and useless areas. The cone-beam data in the corrupted area are then corrected by the forward projection of the pre-reconstruction, while the data in the useless area are set to zero. A generalized Feldkamp algorithm is chosen for the pre-reconstruction. After the correction, the Grangeat-type half-scan based reconstruction of a short object is performed along with several shadow zone interpolation techniques for the final reconstruction. Numerical simulation is conducted to compare the proposed algorithm with a half-scan Feldkamp algorithm.