The development of efficient Cu-based heterogeneous catalysts for CO₂ hydrogenation to methanol has been an appealing subject. Inspired by the concept of inverse catalysts, a series of La₂O₂CO₃/Cu nanorod composites with varying Cu content (denoted as LOC/Cu-x, where x stands for the mass ratio of La and Cu in the catalysts) were prepared by combining coprecipitation and calcination processes. Remarkable composition-dependence of catalytic activity and selectivity were observed when different LOC/Cu-x (x=0.1, 0.2, 0.5, 1, 3, 5) were used to catalyze the CO₂ hydrogenation. The predominant product shifted from methane to methanol with the increasing Cu content. The highest reaction rate (13.3 mmol g_Cu^-1h^-1) and methanol selectivity (85.5 %) were achieved when LOC/Cu-1 was tested at 200 ^oC. The LOC was not active for the reaction, while the Cu itself displayed poor catalytic performance. The Cu-LOC interactions significantly affected the nature of the catalysts, including mutual electron transfer, crystal structure, morphology, porosity, surface Cu valance and capability of adsorbing the reactant gases, etc., which account for the outstanding behavior of the LOC/Cu-1 catalyst. This work provides a new strategy for the design and optimization of Cu-based catalysts.