The interplay between lattice, charge, and spin degree of freedom in antiperovskite compounds gives rise to a range of functional properties including those interesting for spintronics applications. In particular, GaNMn₃ has garnered attention due to possibility of tuning the magnetic phases, such as non-collinear antiferromagnetic Γ_5g phase and collinear ferrimagnetic M-1 phase, by chemical doping and hydrostatic pressure. Here, using first-principles density-functional theory calculations, we explore the anomalous Hall conductivity of antiperovskite GaNMn₃ in different magnetic configurations. In the ferromagnetic M-1 phase, to the anomalous Hall conductivity emerges due to the broken time reversal symmetry, whereas in the non-collinear antiferromagnetic Γ_5g phase with zero magnetization the anomalous Hall conductivity results from the broken time reversal/mirror reflection symmetry combination. We calculate the magnitude of the anomalous Hall conductivity in both phases and discuss the underlying physics associated with this phenomenon.