KCrF(3) has been systematically investigated by using the full-potential linearized augmented plane wave plus local orbital method within the generalized gradient approximation and the local spin density approximation plus the on-site Coulomb repulsion approach. The total energies for ferromagnetic and three different antiferromagnetic configurations are calculated in the high-temperature tetragonal and low-temperature monoclinic phases, respectively. It reveals that the ground state is the A-type antiferromagnetic in both phases. Furthermore, the ground states of the two phases are found to be Mott-Hubbard insulators with the G-type orbital ordering pattern. In addition, our calculations show the staggered orbital ordering of the 3d(x(2) ) and 3d(y(2) ) orbitals for the tetragonal phase and the 3d(z(2) ) and 3d(x(2) ) orbitals for the monoclinic phase, which is in agreement with the available data. More importantly, the relationship between magnetic structure and orbital ordering as well as the origin of the orbital ordering are analyzed in detail.