This paper introduces a novel steel–concrete composite column referred to as the core-steel tube with T-shaped steel reinforced concrete (CSTRC) column, which is composed of a core steel tube with T-shaped steel embedded in a reinforced concrete column. To investigate the mechanical performance of the CSTRC column under eccentric compressive load, the load–deformation response, stress, and strain distribution of CSTRC columns under eccentric load are analyzed by finite element software. Furthermore, the effects of slenderness ratio, concrete and steel strength on the eccentric compression performance of CSTRC columns are also discussed. Finally, a set of formulas for predicting the ultimate strength of the CSTRC columns is proposed. The study results reveal that: (1) The established finite element model accurately predicts bearing capacity and strain development. (2) When the eccentricity is 0.2, the specimen exhibits characteristics indicative of small eccentricity failure. Conversely, when the eccentricity is 0.8, the specimen demonstrates traits associated with large eccentricity failure. Furthermore, as the eccentricity increases, there is a notable decrease in the bearing capacity of the specimen. (3) The slenderness ratio affects the failure mode of the CSTRC columns, with consideration for second-order effects necessary when the ratio exceeds 22. (4) Increasing the concrete strength, steel strength, and steel ratio significantly enhances the ultimate load values of the CSTRC columns. (5) A comparison between calculated and simulated values demonstrates good agreement, validating the accuracy of the proposed method.