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 T_N  =79.5 K, the Cr²⁺  moment orders in an incommensurate antiferromagnetic arrangement, which can be defined by the magnetic propagation vector (½ ± d, ½ ± d,0). The incommensurate-commensurate magnetic transition occurs at 45.8 K and the magnetic propagation vector locks into (½, ½, 0) with the Cr moment of 3.34 (5) µ_B, 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.