The cathode is the key in improving the performance of solid oxide fuel cells (SOFCs) at an intermediate temperature (IT). High performance cathode requires not only large amount of reaction sites, but also efficient transport of gases, electrons and ions, which are characterized by the percolation properties of the cathode. In this paper, the effects of cathode material properties and microstructures on percolation behavior of a composite SOFC cathode are analyzed by a 3D numerically morphological dilation method with controlling contact angles between two types of particles. The proposed model is validated by comparing the present simulation results with data from our previous kinetic Monte Carlo (KMC) simulations. The model is used for calculating the effective conductivity and percolation behaviors of proton-conducting SOFC (H-SOFCs) cathode. Detailed simulations are conducted under different parameters (mean particle radius of composite cathode, volume fraction of electrode and electrolyte materials, bulk material conductivities) to investigate their effects on the important effective ionic conductivity and percolation behavior of the cathode at an IT. The results could help design high performance H-SOFC electrodes.