The nuclear structure systematics of the superheavy nuclei lying at the extreme of mass for Z = 120, and their α-decay half-lives have been studied using the relativistic mean-field (RMF) model. The results are obtained using four different point-coupling parameters after analysing the reliability of these parameter sets for the binding energy of experimentally observed nuclei (Z = 100–118) by comparing them with the available experimental and WS-4 microscopic calculations. The optimal parameter set thus obtained is further used for predicting the Z =120 α-decay chain and decay half-lives.