We report a systemeatic investigation of magnetic anisotropy of quaternary GaMnAsP ferromagnetic semiconductor films by magneto-transport. Hall measurements showed a transition of the easy magnetization direction from in-plane to out-of plane with incorporation of the P into the GaMnAs films. Quantitative information on magnetic anisotropy of the films is obtained by fitting the angular dependence of Hall resistance data to magnetic free energy using the coherent rotation model. Values of magnetic anisotropy parameters show that in-plane anisotropy decreases and out-of-plane anisotropy increases with increasing P content in these films. The out-of-plane magnetic anisotropy in GaMnAsP layers is further enhanced by low temperature annealing. By optimizing the growth and annealing conditions, we were able to obtain a Curie temperature of 125 K in such quaternary films, with strong out-of-plane anisotropy. This study showed that the magnetic anisotropy of the GaMnAsP films can be controlled by adjusting the concentration of the P, and by appropriate post-growth annealing.