Growing evidence has indicated that the global composition distribution plays an indisputable role in interpreting observational data. Three-dimensional general circulation models (GCMs) with a reliable treatment of chemistry and clouds are particularly crucial in preparing for upcoming observations. In attempts to achieve 3D chemistry-climate modeling, the challenge mainly lies in the expensive computing power required for treating a large number of chemical species and reactions. Motivated by the need for a robust and computationally efficient chemical scheme, we devise a mini-chemical network with a minimal number of species and reactions for H_2_-dominated atmospheres. We apply a novel technique to simplify the chemical network from a full kinetics model, VULCAN, by replacing a large number of intermediate reactions with net reactions. The number of chemical species is cut down from 67 to 12, with the major species of thermal and observational importance retained, including H_2_O, CH_4_, CO, CO_2_, C_2_H_2_, NH_3_, and HCN. The size of the total reactions is also greatly reduced, from ~800 to 20. We validated the mini-chemical scheme by verifying the temporal evolution and benchmarking the predicted compositions in four exoplanet atmospheres (GJ 1214b, GJ 436b, HD 189733b, and HD 209458b) against the full kinetics of VULCAN. The mini-network reproduces the chemical timescales and composition distributions of the full kinetics well within an order of magnitude for the major species in the pressure range of 1bar-0.1mbar across various metallicities and carbon-to-oxygen (C/O) ratios. We have developed and validated a mini-chemical scheme using net reactions to significantly simplify a large chemical network. The small scale of the mini-chemical scheme permits simple use and fast computation, which is optimal for implementation in a 3D GCM or a retrieval framework. We focus on the thermochemical kinetics of net reactions in this paper and address photochemistry in a follow-up paper.