Abstract: The gradient representation of the Lorentz-Dirac model and the stability of its equilibrium point are studied. Firstly, the equation of motion of the Lorentz-Dirac model and the definitions and differential equations of the 4 kinds of basic gradient systems and 6 kinds of dual combined gradients are given. Secondly, the feasibility of transforming the reduced Lorentz-Dirac model into a gradient system, an oblique gradient system, and a combined gradient system is verified, and its specific expression is given. Finally, the stability is studied by converting the Lorentz-Dirac equation into a combined gradient system, and an example is used to verify the application of the results.