Porous networks provide the main transport channels to the active media, which will damage the microstructure and then lead to a subsequent reduction in the strength, serviceability and aesthetic of porous materials. The connectivity of the porous network plays an essential role in the transport properties of these active media. In statistic physics, the percolation threshold ϕc is usually used to describe the formation of long-range connectivity in the system and it has been demonstrated that ϕc of porous network is highly depended on the geometrical shape of the pores. However, the previous studies focused on the symmetric pores such as spheres, ellipsoids and spherocylinders, etc. How the particle asymmetry affects the percolation behaviour of the porous network and then influences the transport properties of materials is still undiscovered. In this work, a family of asymmetric ovoids is introduced. By combining the geometric model of ovoid with the Monte Carlo simulation, a series of porous composite composed of congruent overlapping pore of asymmetrical ovoids are modelled. Then, the percolation thresholds ϕc of composites are obtained by an excluded volume based approximation formula. Furthermore, a general percolation-based effectivemedium approximation is adopted to theoretically study the ionic diffusivities of the twophase porous composites considering their percolation behaviours. The results shed light on the intrinsic and complex interplay of components, structure and transport properties in composites, which can provide some guidance for the development of percolation theory and the design of composites.