Transition metals with desirable valence states have been proposed as efficient non-noble-metal electrocatalytic systems for selective water splitting. In this work, two-dimensional (2D) nitrogen-doped leaf-like carbon matrix arrays functionalized with multi-valence-state transition metal (cobalt) hybrids were successfully prepared by in situ calcination of the corresponding bimetallic leaf-like zeolitic imidazolate framework (ZIF-L) in an inert atmosphere. The 2D morphology of the matrix along with the particle size and surface valence state of the anchored particles has been successfully controlled via precisely adjusting the Co2+/(Zn2+ + Co2+) ratio in the bimetallic ZIF-L precursor. Electrochemical measurements show that the kinetics of and stability towards the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) are highly dependent on the particle size as well as the valence states. It was found that the particles with sizes less than 60 nm exhibit mixed Co0/Co2+ valence states, and therefore demonstrate bi-functional electrocatalytic performance. The theoretical simulations revealed that the bi-functional electrocatalytic activity should be attributed to the synergetic effect of mixed Co0/Co2+ and electronic coupling in the hybrids, which are of benefit to the catalytic kinetics and dynamics. High HER and OER activities of the hybrids have been verified, in which overpotentials of 171 and 280 mV to deliver a current density of 10 mA cm-2 for the HER and OER, respectively, were achieved. The obtained correlation between non-noble-metal-based carbon composites and HER/OER activities may be exploited as a rational guideline in the design and engineering of electrocatalysts.