Effective integration of CNTs and heteroatom-doped graphene can produce a new functional carbons that combines the extraordinary properties of heteroatom-doped graphene (e.g., catalytic activity, and huge exposed field) with those of CNTs (e.g., mechanical stability, and high electronic conductivity). Herein, we report a straightforward method to manufacture a metal-free, hierarchically porous and N/S co-doped CNT-graphene 3D framework via one-step pyrolysis of the guanine-sulfate and OCNTs. The usage of guanine-sulfate as carbon precursor can yield very regular (2D nanosheet) and in situ nitrogen-doped carbons. By combining with OCNTs, the as-obtained graphene is found to strongly couple with the surface of CNTs, achieving the uniform distribution of both components. Such 3D hybrid shows high activity toward a set of important electrochemical reactions and high-performance in Zn-air batteries. Systematic electrochemical studies indicate the indispensability of both the optimal nitrogen configuration and well-developed porosity for excellent ORR/OER/HER performance. The amount of pyridinic-N and graphitic-N, rather than the total nitrogen content, has a more positive effect on ORR activity, particularly for the onset potential; while the favorable pore size distributions might guarantee a much well-developed diffusion-limited current region and considerable diffusion-limited current value. These results undoubtedly could provide meaningful guidance to develop highly efficient electrocatalysts.