The effect of fluid axial thermal conduction on one-dimensional liquid metal natural circulation and its linear stability was performed through nondimensional analysis, steady-state assessment, and linear perturbation evaluation. The Nyquist criterion and a root-search method were employed to find the linear stability boundary of both forward and backward circulations. The study provided a relatively complete analysis method for one-dimensional natural circulation problems with the consideration of fluid axial heat conduction. The results suggest that fluid axial heat conduction in a natural circulation loop should be considered only when the modified Peclet number is [approximately]1 or less, which is significantly smaller than the practical value of a lead liquid metal-cooled reactor.