Abstract: Based on the dynamic stability theory of an elastic system, parametric vibration equations of laced and battened lattice columns subject to a periodic load under high temperature (fire) condition were established respectively by adopting the energy method and Hamilton principle. Galerkin's method was used to convert the partial differential equations into second order ordinary differential Mathieu equations, and then the dynamic instability regions surrounded by periodic solutions were obtained. The dynamic stability problems of parametric vibration were discussed about two kinds of axial compression lattice columns. Through analyzing the influences of slenderness ratio, constant load and temperature etc. on the dynamic instability regions of axial compression lattice column, reference basis for the dynamic analysis and design on high temperature (fire) condition in structure engineering is provided.