The magnetic, electronic, and topological properties of GdPtBi were systematically investigated using first-principles density functional theory (DFT) calculations. Various magnetic configurations were examined, including ferromagnetic (FM) and antiferromagnetic (AFM) states, with particular focus on AFM states where the Gd magnetic moments align either parallel (AFM‖) or perpendicular (AFM⊥) to the [111] crystal direction. For AFM⊥, the in-plane angles ϕ were varied at ϕ = 0°, 15°, and 30° (denoted as AFM⊥,ϕ=0°, AFM⊥,ϕ=15°, and AFM⊥,ϕ=30°, respectively). The ground-state magnetic structure of GdPtBi was validated through dipolar magnetic field calculations at the muon sites, corroborating the internal magnetic fields observed in muon spin relaxation (μSR) experiments. The results indicate that the AFM⊥,ϕ=30° configuration aligns with the μSR-measured internal field. The DFT-calculated band structure and Berry curvature reveal that AFM⊥ belongs to the triple-point semimetals (TPSMs) where the triple-point nodes positioned along the Z-Γ-Z and F-Γ-F paths have energies that shift as the spin-orbit coupling strength varies with ϕ. Notably, this shift in triple-point energy corresponds to a significant change in the anomalous Hall conductivity (AHC, σxy), with a difference of 75.06 Ω-1 cm-1 at the Fermi energy between AFM⊥,ϕ=0° and AFM⊥,ϕ=30°. These findings highlight the potential for controlling the AHC through precise manipulation of the AFM structure.