Magnetic behavior of La_{0.75}Pr_{0.25}Co_{2}P_{2} was investigated by a combination of magnetic measurements, magneto-optical imaging, neutron diffraction, and x-ray absorption spectroscopy, including x-ray magnetic circular dichroism. The material crystallizes in the ThCr_{2}Si_{2} structure type and exhibits three consecutive magnetic phase transitions. At 167 K, the Co magnetic moments order ferromagnetically in the ab plane of the tetragonal crystal structure. At 66 K, a ferromagnetic ordering of Pr(4f) moments parallel to the c axis causes a rotation of the Co(3d) moments towards the c axis in the direction opposite to the Pr moments, thus forming a noncollinear ferrimagnetically ordered structure and switching the direction of the total magnetization from the ab plane to the c axis. The third magnetic transition observed at 35 K is likely associated with the establishment of the collinear ferrimagnetic order along the c axis.