Abstract The magnetic ground states in highly ordered double perovskites LaSr 1− x Ca x NiReO 6 ( x  = 0.0, 0.5, 1.0) are studied in view of the Goodenough-Kanamori rules of superexchange interactions in this paper. In LaSrNiReO 6 , Ni and Re sublattices are found to exhibit curious magnetic states separately, but no long range magnetic ordering is achieved. The magnetic transition at ~255 K is identified with the independent Re sublattice magnetic ordering. Interestingly, the sublattice interactions are tuned by modifying the Ni-O-Re bond angles through Ca doping. Upon Ca doping, the Ni and Re sublattices start to display a ferrimagnetically ordered state at low temperature. The neutron powder diffraction data reveals long range ferrimagnetic ordering of the Ni and Re magnetic sublattices along the crystallographic b- axis. The transition temperature of the ferrimagnetic phase increases monotonically with increasing Ca concentration.