Developing the highly efficient and durable non-precious metal electrocatalysts by taking advantage of inexpensive and abundant resources is of paramount importance for the widespread application of energy conversion and storage techniques such as fuel cells and metal-air batteries. Herein, the sponge-like unadulterated carbontube-graphene complexes (D/G-CTs-1,000) with multifarious intrinsic defect active sites are fabricated by boric acid-hydrothermal and pyrolysis treatments. The close contact or juncture between open nanotubes and few-layer graphene in D/G-CTs-1,000 constructs the hierarchical networks with plentiful channels, the larger surface area and outstanding conductivity. As a result, the as-prepared D/G-CTs-1,000 electrocatalyst exhibits an excellent trifunctional electrocatalytic performance for oxygen reduction reaction (ORR), oxygen evolution reaction (OER) and hydrogen evolution reaction (HER). The primary Zn-air batteries and overall water splitting system using D/G-CTs-1,000 as the electrode materials delivers higher power density outperforming the advanced Pt/C-based batteries and the overall water splitting performance comparable to those using the non-precious metal/carbon-based materials as electrode. This work provides a universal and efficient synthetic strategy to produce the unadulterated carbons with high activity and long-time durability as trifunctional electrocatalysts and promote the widespread applications of metal-free electrocatalysts in sustainable energy conversion technology.