H+ based solid oxide fuel cell (SOFC) composite cathodes are generally agreed to be of quite different relationships among the microstructure parameters, electrode properties and detailed working processes from the conventional O2--SOFC composite cathodes. In this paper, the percolation theory is significantly generalized and developed to suit most of the typical H+-SOFC composite cathodes with e(-)/H+, e(-)/O2- or e-/H+/O2- mixed conducting characteristics; not just limited to the BCZY, SDC and LSCF materials. It provides an easy way to investigate the effect of microstructure parameters on the H+-SOFC electrode characteristics in quantity. The studied electrode properties include: i) the potential coexisting sites of O-2, e(-), and O2- transport paths for the oxygen reduction; ii) the potential coexisting sites of O2-, H+ and H2O transport paths for the vapor formation; iii) the effective e(-), O2-, and H+ conducting and gas diffusing capabilities of the composite cathodes, and so on. It will be helpful for the H+-SOFC composite cathode manufacture to achieve the expected properties. Furthermore, it is also an important step for the developing of the multiphysics-model in manuscript part B to study the effect of the microstructure parameters on the H+-SOFC working details. (C) 2015 Elsevier B.V. All rights reserved.