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While the carrier-mediated ferromagnetism on GaMnAs has been thoroughly studied in the past, the origin of anomalous Hall effect (AHE) in magnetic III-V systems remains elusive, particularly for the quaternary GaMnAsP. We have thus measured the AHE in a series of GaMnAsP alloys grown by molecular beam epitaxy with varying amounts of phosphorus, both as-grown and annealed. We carried out extensive measurements of transverse and longitudinal resistivity as a function of both magnetic field and temperature. By applying a modified Brillouin-Weiss model for the magnetization, we decompose the AHE into an “extrinsic” contribution (due to scattering) and a dominating “intrinsic” contribution (due to the Berry curvature). Our data strongly indicates that the influence of the intrinsic mechanism is important in samples with low phosphorus content. Importantly, we find that the amount of the intrinsic contribution is tunable by controlling the phosphorus concentration in GaMnAsP alloys. Consequently, our results suggest that the valence bands of III-Mn-V compounds could host a strong Berry curvature, possibly driven by the strain effects that are known to occur in GaMnAsP grown on GaAs.