Abstract: Preconditioning is the key to the efficiency and convergence of JFNK method. The preconditioning process of JFNK method was investigated based on an eigenvalue problem for high temperature gas-cooled reactor (HTGR) neutron diffusion, including the regions such as reactor core, graphite reflector and carbon brick. The Jacobian matrix was simplified according to the physical characteristics of matrix elements. The different preconditioners were obtained by the linear preconditioning methods such as ILU and SIPLU. The preconditioning features such as preconditioning quality, sparsity and calculation time were analyzed. The results indicate that the block Jacobian matrix is a good approximation to the original Jacobian matrix, and the former can constructe a simple and adaptive original Jacobian matrix while maintaining the coupling information inside each neutron energy group. SIPLU preconditioner can reach a high preconditioning quality and efficient simulation in solving this kind of HTGR neutron diffusion problem.