The streamer discharge is the inaugural stage of gas discharge, and the electron average energy directly determines the electron collision reaction rate, which is a key parameter for studying the streamer discharge. Therefore, taking into account the electron average energy, this work establishes a fluid chemical reaction model to simulate and study the streamer discharge’s evolution course in a 5 mm rod-plate gap, considering 12 particles and 27 chemical reactions. It introduces the electron energy drift diffusion equation into the control equation, and analyzes the temporal and spatial changes of electron average energy, electric field intensity and electron density with the change of rod radius and voltage, the effects of voltage and rod radius on the course of streamer discharge can be reflected more comprehensively by combining the average electron energy. Three different values of 0.3 mm, 0.4 mm and 0.5 mm are set for the rod radius, and three different values of 5 kV, 6 kV and 7 kV are set for the voltage. The influence of the excited reaction on the discharge of the streamer is studied. The findings indicate that as voltage raises, the streamer head’s electron density, electric field, and electron average energy all rise, and the streamer develops more quickly. When the rod radius increases, the streamer head’s electron density, electric field, and electron average energy all decrease, and the streamer’s evolution slows down. When the excitation reaction is added to the model, the electron average energy, the magnitude of the electric field and the density of electrons decrease, and the evolution of streamer slows down. The increase of electron average energy will lead to the increase of electric field strength and electron density, and the development of streamer will be faster.