The spin-crossover (SCO) phenomenon is an active area of research. This paper describes the synthesis of an Fe-Ag Hofmann-type complex, {Fe(4-methylpyrimidine)2[Ag(CN)2]2}, which demonstrates a one-step SCO and single-layer Hofmann-type structure with Ag-N interactions and no Ag-Ag interactions, which is strikingly different from the previously synthesized complex {Fe(4-methylpyrimidine)2[Au(CN)2]2} that contains Au-Au interactions and no Au-N interactions. This difference can be explained in terms of the lack of relativistic effect in the Ag atoms and the different cooperative effects caused by their different structures. A scan-rate-dependent hysteresis is observed using magnetic measurement whereas not using 57Fe Mössbauer spectroscopy, suggesting that the spin transition is relatively slow.