The discrete ordinates method (Sn) is the most widely used technique to obtain numerical solutions of the linear Boltzmann equation, and therefore to evaluate radiation fields and dose rates in nuclear devices. However, it is well known that this method suffers from slow convergence for problems characterized by optically thick media and scattering ratio close to unity. To address this issue we have developed a new preconditioning algorithm based on the even-parity simplified Sn (ep-ssn) equations. The new method is based on the flux acceleration simplified transport (fast) algorithm which is implemented into the pentran-ssn code system. The code system is designed for parallel computing architectures; pentran-ssn features spatial, angular, and energy domain decomposition algorithms. The fast preconditioner is parallelized with a spatial domain decomposition algorithm. In this paper, our objective is to test the performance of the new preconditioning system for a three-dimensional shielding calculation based on the venus-2 mox-fueled benchmark problem, issued by OECD/NEA (Organization for Economic Co-operation and Develpment/Nuclear Energy Agency.