Conductive electrical tree, as the final stage of electrical tree growth, has a significant impact on the properties of insulating materials. In order to simulate the growth morphology and bifurcation process of conductive electrical tree, a bifurcation scale model of electrical tree is proposed based on fractal theory. The influence of electric field and randomness on its growth is considered, and then the finite element method is used to simulate the electrical tree in epoxy resin materials. The fractal dimension of each bifurcation in the dynamic growth process of electrical tree is recorded. The results show that the simulated tree obtained by this method is similar to the clump shape, and gradually transits to the branch shape in the late growth stage. The fractal dimension calculated by the box counting method shows an upward trend, and there is only a small fluctuation in the 5~9 bifurcations of the electrical tree. Therefore, the simulation model with fractal structure is helpful to understand the bifurcation process of electrical tree growth from the microscopic electric field level, and provides a reference for the study of measures to inhibit the growth of electrical tree.