Another family of complex network—— the generalized Farey organized network pyramid (GFONP) is introduced. Three typical determinate constructional algorithms are shown, and corresponding topological characteristics are studied by theoretical and numerical analysis. The results show that the three determinate GFOPN networks have similar characteristics, i.e. their degree distributions follow exponential distribution in form, the clustering coefficient of the network decreases to a constant value with the step t increasing, the resulting network evolves from one with disassortative to one with assortative coefficient with increasing t, and the degree-degree correlation coefficient tends to a positive constant. This may lead to potential applications of the network of pyramidal structure.