A dual-phase ceramic membrane consisting of gadolinium-doped ceria (GDC) as an oxygen ion conducting phase and $MnCo_2O_4$ as an electron conducting phase was fabricated by sintering a GDC and $MnCo_2O_4$ powder mixture. The $MnCo_2O_4$ was found to maintain its spinel structure at temperatures lower than $1200^{circ}C$. (Mn,Co)(Mn,Co)$O_4$ spinel, manganese and cobalt oxides formed in the sample sintered at $1300^{circ}C$ in an air atmosphere. XRD analysis revealed that no reaction phases occurred between GDC and $MnCo_2O_4$ at $1200^{circ}C$. The electrical conductivity did not exhibit a linear relationship with the $MnCo_2O_4$ content in the composite membranes, in accordance with percolation theory. It increased when more than 15 vol% of $MnCo_2O_4$ was added. The oxygen permeation fluxes of the composite membranes increased with increasing $MnCo_2O_4$ content and this can be explained by the increase in electrical conductivity. However, the oxygen permeation flux of the composite membranes appeared to be governed not only by electrical conductivity, but also by the microstructure, such as the grain size of the GDC matrix.