Previous investigations proved the unsafety of the current design guidelines in Annex H of EN 1994-1-2 for the calculation of the fire resistance of slender concrete-filled steel tubular (CFST) columns. In this paper, a new simplified design method based on the general rules in Clause 4.3.5.1 of EN 1994-1-2 is presented for correcting this inaccuracy. For the development of the method, an extensive parametric study consisting of about 20.500 analysis cases was carried out by using numerical models, which in turn were validated against a wide range of experimental results. The proposed method provides a significant extension over the current EN 1994-1-2 applicability limits, reaching high member slenderness, large eccentricities and being valid for all the commercially available geometries, including elliptical hollow sections. The design proposal is divided into two parts: thermal, where a simplified cross-sectional temperature field can be obtained based on equivalent temperatures for the composite section constituents, and mechanical, where a full method for evaluating the ultimate buckling load in the fire situation is given. The proposed method is valid for axially and eccentrically loaded columns, accounting for eccentricities on both minor and major axis and reaching large eccentricities of e/D = 1. Finally, it is proved that the proposed method provides safe predictions as compared to experimental results and meets the CEN/TC250/SC4 accuracy criteria.