The concrete confinement provided by the circular steel tubes improves the performance of circular concrete-filled double steel tubular (CFDST) columns, which have increasingly been employed as high-performance structural members in tall buildings. This paper presents computational and design models for the simulation and design of high strength CFDST slender columns composed of circular thin-walled sections that are eccentrically loaded. The formulation of the computational model is described, which takes into account the influences of concrete confinement, geometric imperfection, second-order, gradual plasticity of steel, and geometric and material nonlinearities. The inverse quadratic method is implemented in computational algorithms which solve the highly nonlinear equilibrium function of slender CFDST circular columns. The computations are compared with experimentally measured results to validate the mathematical modeling procedure developed. The behavior of slender circular CFDST columns made of high-strength concrete is investigated by utilizing the developed computational model taking into consideration the important material and geometric parameters. Proposed are design models that determine the ultimate loads of CFDST slender columns loaded concentrically and the axial load-moment strength interaction curves of slender thin-walled CFDST columns under eccentric loads. It is shown that the computational simulation method proposed can efficiently and accurately capture the experimentally measured behavior of CFDST slender columns. The design models give good strength predictions of CFDST columns and can be employed in designing CFDST composite columns.