Determination of the aircraft lightning attachment points which can provide the basis for the design of aircraft lightning protection, is a prerequisite for the division of lightning strike zones and the lightning test of aircraft components. In this paper, a novel numerical simulation method based on fractal theory is presented to simulate lightning attachment points on airplane. Firstly, the discharge gap distance, lightning starting coordinates, aircraft attitudes, discharge times and other parameters are determined according to the relevant provisions about aircraft lightning attachment point test in standard SAE-ARP5416. Then, according to the fractal theory, the dielectric breakdown model is used to simulate the fractal growth of the lightning leaders, which accords with physical mechanisms and geometric characteristics of nature lightning. Finally, considering the case where the aircraft itself triggers the bi-directional leader, we obtain the distribution of aircraft lightning attachment points. Because the probability distribution of lightning attachment points on aircraft F-4 obtained through the simulating is almost in line with those obtained through actual aircraft flight test and laboratory test, the proposed method is verified. The proposed method provides a potential way of simulating the lightning attachment points on aircraft. And this method can be used as the foundation of the aircraft lightning protection design and future related research work.