Accurate modeling of high-impedance arc fault (HIAF) is of great significance for studying the characteristics of arc fault and suppressing its harm. In traditional arc models, the arc column is usually considered a cylindrical channel with constant length and diameter. However, the arc-burning process is susceptible to the environment. The changes in arc length and diameter present complex characteristics. Therefore, this study proposes a new HIAF model for distribution networks based on the arc's dynamic geometry dimension (DGD). First, the arc length, diameter, and field strength expressions are improved based on the classical cybernetic model. Next, an automatic parameter optimization method for the DGD model is proposed, and then this model is compared with existing advanced models. After that, the effects of the variable parameters of this model on arc characteristics are analyzed. Finally, the practical application effect of this model is tested. The experimental results show that the DGD model can accurately describe the dynamic arc development process, approximate the given arc waveform closely, and generate high-quality samples, which has certain advantages.