The cathode is the key in improving the performance of solid oxide fuel cells (SOFCs). In operation, oxygen and molecules and electrons are transported through the pores and electronic particles respectively to the three-phase boundaries (TPBs), where they react to produce oxygen ions. Subsequently, oxygen ions are conducted from the TPBs to the dense electrolyte through ionic particles. Efficient operation of SOFC cathode thus requires large length of TPB, fast gas transport in pores and efficient conduction of electrons/oxygen ions in the electronic/ionic particles. All the above-mentioned properties heavily depend on the cathode microstructure, which is formed during the sintering process. Since the composite cathode electronic/ionic conduction is one major voltage loss, it is necessary to verify whether the optimal sinter microstructure corresponding to the peak TPB length can also yield high electronic/ionic conductivities or not. In this article, effects of geometrical parameters of microstructures (contact angle, porosity) on electronic/ ionic conductivities of composite SOFC cathodes are analyzed by a 3D morphological dilation method with controlling different contact angles between two types of particles or porosity. The composite cathode powder compacts are formed by randomly dropping spherical particles into the computational domain. Detailed simulations are conducted under different contact angles or porosities for investigating whether peak TPB length can also yield higher electronic/ ionic conductivities. Optimal contact angle rangle is verified to be 30~35º and better tortuosity factor corresponding to optimal volume TPB length.