Effect of chemical reaction on Li-ions diffusion and diffusion-reaction-induced stresses in a spherical electrode is studied, considering the reaction rate determined by the relation between hydrostatic stress and activation enthalpy, to derive new diffusion equation. The coupling equations of diffusion and mechanics are developed to obtain numerical simulation results of Li-ion concentration and diffusion-reaction-induced stress under galvanostatic operation during lithiation. Results indicate that chemical reaction can slow down the diffusion process and lead to the increase of radial stress and hoop stress, which is enhanced as the reaction rate constant increases. The effect of hydrostatic stress in activation enthalpy can change the reaction rate, resulting in distribution difference of the Li-ion and reaction product concentration and the decline of the radial and hoop stress.