In order to investigate the mechanical behavior of special-shaped reinforced concrete composite columns encased with GFRP core columns (EGCSSCs) subjected to axial load, twenty-seven full-scale EGCSSCs were designed with varying parameters: axial compressive strength of core concrete (fcc), axial compressive strength of peripheral concrete (fco), thickness of GFRP tube (tgfrp), ratio of longitudinal reinforcement (ρv), stirrup ratio (ρs) and GFRP ratio in the cross-section (α). The three-dimensional finite element refined models of EGCSSCs were established by ABAQUS finite element software, and the response of EGCSSCs under axial load was studied based on the verification of finite element modeling. The influence of different parameters on the ultimate axial compressive strength (Nus), initial stiffness (K), and ductility index (µ) of EGCSSCs was obtained, and the typical failure mode of EGCSSCs was clearly described. The results showed that the main failure mode of the EGCSSCs subjected to axial load was bulging outward at the middle of the EGCSSCs, showed yielding of the longitudinal steel bars, and was crushing both ends of the peripheral concrete. When the column was damaged, the peripheral concrete reached peak stress earlier than the core concrete. All specimens exhibited excellent load-carrying capacity and good ductility. Moreover, with the existence of GFRP core columns, the Nus and µ of the columns were increased by 11.61% and 140.86%. In addition, K increased with the increase in fcc, fco, tgfrp and α, and the largest increments were 23.99%, 50.54%, 21.77%, and 34.19%, respectively. µ decreased with the increase in fcc and fco, which decreased by 14.05% and 40.28%, respectively. By using statistical regression and introducing the constraint effect coefficients and the reduction coefficient, the calculation formula for the axial compression-bearing capacity of EGCSSCs was derived, which could lay a foundation for the popularization and application of this kind of composite column in practical engineering.