Slender rectangular thin-walled concrete-filled steel tubular (CFST) columns in composite building structures exposed to fire may experience the interaction of local and global buckling. Numerical investigations on the interaction buckling responses of such columns under fire exposure have been rarely reported. This paper describes a fiber-based computational model for the prediction of the fire-resistance and interaction responses of local and global buckling of concentrically-loaded slender CFST columns made of rectangular sections exposed to fire. The thermal analysis is undertaken to calculate the distribution of temperatures in the column cross-section considering the effects of the air gap between concrete and steel, exposure surface emissivity as well as moisture content in concrete. The local and post-local buckling models proposed previously for steel tube walls at elevated temperatures are incorporated in the inelastic analysis of cross-sections to model the progressive post-local buckling. The global buckling analysis of slender CFST columns exposed to fire accounts for the effects of material and geometric nonlinearities as well as local buckling. Efficient computational procedure and solution algorithms are developed to solve the nonlinear equilibrium dynamic functions of loaded slender CFST columns exposed to fire. Independent experimental and numerical results on slender CFST columns are utilized to validate the computational model. The interaction behavior of local and global buckling and fire-resistance of slender rectangular CFST columns are investigated. It is shown that the developed computational model provides a reasonably accurate and efficient method for the prediction of the interaction buckling responses as well as the fire-resistance of slender CFST columns subjected to axial loading and fire.