KCrF3 represents another prototypical orbital-ordered perovskite, where Cr2+ possesses the same electronic configuration of 3d4 as that of strongly Jahn-Teller distorted Mn3+ in many colossal magnetoresistance manganites. The crystal and magnetic structures of KCrF3 compound are investigated by using polarized and unpolarized neutron powder-diffraction methods. The results show that the KCrF3 compound crystallizes in tetragonal structure at room temperature and undergoes a monoclinic distortion with the decrease in temperature. The distortion of the crystal structure indicates the presence of cooperative Jahn-Teller distortion which is driven by orbital ordering. With decreasing temperature, four magnetic phase transitions are observed at 79.5, 45.8, 9.5, and 3.2 K, which suggests a rich magnetic phase diagram. Below TN=79.5K , the Cr2+ moment orders in an incommensurate antiferromagnetic arrangement, which can be defined by the magnetic propagation vector ((1)/(2)±delta,(1)/(2)±delta,0) . The incommensurate-commensurate magnetic transition occurs at 45.8 K and the magnetic propagation vector locks into ((1)/(2),(1)/(2),0) with the Cr moment of 3.34(5)muB , aligned ferromagnetically in (220) plane, but antiferromagnetically along [110] direction. Below 9.5 K, the canted antiferromagnetic ordering and weak ferromagnetism arise from the collinear antiferromagnetic structure while the Dzyaloshinskii-Moriya interaction and tilted character of the single-ion anisotropy might give rise to the complex magnetic behaviors below 9.5 K.