Sb2O3 and Co3O4 as potential anode materials for Li- and Na-ion batteries exhibit high theoretical capacities and excellent electrochemical stability; however, volume expansion, exfoliation and poor electronic conductivity affect the electrochemical performance to some extent. Here, we design dual metal oxide hybrid composites by one- and two-step solvothermal processes, in which Co3O4 with Sb2O3 traps Li+ ions and carbon nanotubes (CNTs) as a network guarantee for electron transport. Sb2O3/CNTs/Co3O4 and Sb2O3/Co3O4/CNTs composites exhibit different morphologies, particles sizes and Li+/Na+ storage performance. The Sb2O3/CNTs/Co3O4 composite showes initial capacities of 1790 and 1450 mAh g-1 after 100 cycles as the anode for a Li-ion battery. The capacity retention of the Sb2O3/Co3O4/CNTs composite is better than the Sb2O3/CNTs/Co3O4 composite for Na-ion storage. With charge/discharge cycles, the transition reaction of Sb2O3 and Co3O4 to Sb and Co repeats, leading to a homogenous distribution in CNTs and further growth of the nanoparticles. This work provides new insights into the design of high-capacity anodes for Li- and Na-ion storage by adjusting their composition and morphology.