Abstract: Starting from the Bernstein's hydromagnetic energy principle, a general analysis is presented on the stability of a kind of one-dimensional force-free magnetic fields with singular current density surfaces and a single parameter in the cylindrical coordinates. The results obtained show that there exist stable and unstable regions in the parameter space. Their stability is determined solely by the radial distribution of the magnetic pitch in the neighborhood of the cylindrical axis, and irrelevant to the presence of the singular current density surface at the boundary.