High-strength square concrete-filled double steel tubular (CFDST) slender beam-columns with a circular internal steel tube subjected to eccentric loads may undergo interaction local-global buckling. No computational studies on the interaction local-global buckling of slender square CFDST beam-columns have been reported and their behavior has not been fully understood. This paper describes a mathematical model for the simulation of the interaction local-global buckling behavior of square high-strength CFDST slender beam-columns under axial compression in combination with uniaxial bending. The mathematical model is formulated by the fiber approach, accounting for confinement provided by the internal circular steel tube, and geometric and material nonlinearities. An incremental-iterative numerical procedure is designed to quantify the local-global interaction buckling responses of slender CFDST columns. Efficient numerical solution algorithms implementing the inverse quadratic method are developed for solving the nonlinear equilibrium dynamic functions of CFDST columns. The formulation proposed is verified by existing experimental data on CFDST columns as well as double-skin concrete-filled steel tubular (DCFST) slender columns. The developed computational model is employed to study the local-global interaction buckling behavior of CFDST columns made of high-strength materials with various important parameters. Simplified design models are proposed for determining the ultimate axial strengths of slender square CFDST columns under axial compression and the interaction curves of CFDST slender beam-columns loaded eccentrically. It is demonstrated that the computational and design models predict well the interaction local-global buckling behavior and strength of slender square CFDST beam-columns.