An enhanced positronium (Ps) formation in low-temperature polymers has been widely observed. The additional positronium formation is due to shallow trapped electrons in them. Positron annihilation lifetime spectroscopy was applied to investigate the Ps formation in a series of polymers, such as low-density polyethylene, ethylene-methyl methacrylate copolymers with various methyl methacrylate contents, and pure poly(methyl methacrylate) at low temperature. An analysis of the experimental data based on simple kinetic equations enables one to understand the Ps formation mechanism in polymers during low-temperature positron annihilation experiments as functions of the temperature and elapsed time. Good fittings of the experimental data were obtained. The fitting parameters seemed to show clear physical meanings.