In recent years, there has been a notable surge in proposals for various forms of special-shaped concrete-filled steel tubular (CFST) columns. Despite various methods developed by researchers for determining the bearing capacity of multi-cell special-shaped CFST columns under different loading conditions, these methods remain lack unified. In this study, FE models were developed to simulate performances of improved multi-cell L-shaped CFST (ML-CFST) column under compression and bending. Parametric analyses have been performed to evaluate impact of various factors, including steel yield strength fy, compressive strength of concrete fcu, steel thickness t, loading direction θ, web height c, and axial load ratio n, on performances of ML-CFST columns. The findings of study indicate that the unidirectional flexural capacity of ML-CFST member exhibits a nearly linear relationship with the variables of t, fy, and c, with a minimal impact observed from fcu on flexural capacity. The width of extended section b, fcu, fy, and t have a certain effect on flexural capacity at any angle, particularly fy, t, and b. While fcu, fy, and t exert some influence on N/Nu-M/Mu correlation curves, their influences are marginal compared to the loading direction, which is the predominant influencing factor. Additionally, Mx0/Mπ/4-My0/M3π/4 curves gradually protrude outward with the increase in n. The effects of t, fy, and fcu on the shape of Mx0/Mπ/4-My0/M3π/4 curve were relatively insignificant. Simplified unidirectional flexural capacity calculation models were proposed based on stress analysis of cross-section under ultimate states. Given that flexural capacities estimated by simplified calculation model are slightly conservative, it is recommended to increase the flexural capacities by 10 %. Furthermore, an elliptical equation was formulated to predict the flexural capacity at any angle, with the predictions being slightly conservative. Based on ultimate equilibrium theory, a simplified calculation method was presented to predict unidirectional eccentric bearing capacities of ML-CFST columns. Through regression analysis, a simplified calculation method expressed as polar coordinate form for biaxial eccentric bearing capacity was established, with calculated values aligning well with FE results.