A mathematical model using the fiber approach is presented in this paper for quantifying the strength and fire-resistance of eccentrically loaded slender concrete-filled steel tubular (CFST) columns with rectangular sections incorporating the interaction of local and global buckling. The model utilizes the thermal simulator to ascertain the temperature distribution in cross-sections, and the nonlinear global buckling analysis to predict the interaction responses of local and global buckling of loaded CFST slender columns to fire effects. The initial geometric imperfection, air gap between the concrete and steel tube, tensile concrete strength, deformations caused by preloads, and temperature-dependent material behavior are included in the formulation. The computational theory, modeling procedure and numerical solution algorithms are described. The computational model is verified by existing experimental and numerical results. The structural responses and fire-resistance of CFST columns of rectangular sections exposed to fire are investigated. The mathematical model proposed is demonstrated to be an efficient computer simulator for the fire-performance of slender CFST columns loaded eccentrically.