At present, although there is some studies about the theoretical calculation studies of Zn1-xTMxO1-yNy(TM=Al, Ga, In) p-type doped have been reported. But, they are random doping and without considering the asymmetry of ZnO preferred orientation to doping. Therefore, Six different supercell models Zn1-xTMxO1-yNy (TM = Al, Ga, In. x = 0.0625, y = 0.125) which proportion is TM:N = 1:2 and preferred orientation to co-doped have been constructed based on the first-principles plane wave ultra-soft pseudo potential method of density function theory, in this study.Then calculate the geometric optimization, State density distribution and Band structure distribution for all models, respectively. Results indicate that with the condition of heavily doped and preferred orientation to co-doped, in the same kind of preferred orientation co-doping systems, the electrical conductivity of the system which TM-N bond along the c-axis direction is greater than it perpendicular to the c-axis. In the different kinds co-doping ZnO systems which TM-N bond along the c-axis direction, The co-doping systems of In-N bond along the c-axis direction has the strongest conductivity and the lowest ionization energy and the largest Bohr radius. It is more favorable for electrical conductivity of p-type ZnO. This study can be a theoretical guidance for improve the electrical conductivity of which design and preparation TM:N=1:2 ratio preferred orientation co-doping ZnO systems.