Purpose: To accelerate the image reconstruction process for iterative algebraic reconstruction techniques using a cylindrical voxelization method. Methods: Iterative image reconstruction has many advantages, such as noise reduction and mitigation of approximate cone reconstruction artifacts, over analytical image reconstruction. But its high computational cost prohibits its use in many clinical applications, such as image guided radiotherapy (IGRT). The system matrix used in iterative reconstruction is often too large to store on the hard drive or in RAM. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as cone beam computed tomography (CBCT) and tetrahedron beam computed tomography (TBCT). In this study, the iterative simultaneous algebraic reconstruction technique (SART) algorithm using a cylindrical voxelization method is developed for TBCT. The new algorithm takes advantage of the symmetries of the axial scanning geometry used in TBCT and greatly reduces the size of the system matrix. An additional step is needed for interpolating the cylindrical data onto a Cartesian grid. The reconstruction algorithms were tested with numerical phantoms as well as patient CT data. Results: The system matrix with the cylindrical voxelization method is compact and can be easily stored in the computer RAM. SART reconstruction using the cylindrical voxelization method was implemented for the TBCT. The FOM results for the cylindrical voxelization method were slightly better than for the Cartesian voxelization. The cylindrical method was able to provide a speedup of 40 times over the traditional Cartesian method and to provide a reduction of two orders of magnitude in the storage requirement for the system matrix. Conclusion: Image reconstruction using a cylindrical voxelization method was able to provide a significant improvement in the reconstruction speed while maintaining the image quality provided by the conventional reconstruction method using a Cartesian image grid. This work is partially supported by NIH SBIR contract #HHSN261201100045C.