The competition and cooperation of radiation domain reflects the competitiveness of the airports in the multi-airport system. Based on Lotka-Volterra model, this paper studies the competition equilibrium of the cross hinterland for the regional multi-airport system. Taking the comprehensive strength of airports as the influencing factor, the market share of each airport in the cross hinterland is selected as the dependent variable to solve the competitive stable state and the required conditions between the two airports. Taking the cross hinterland of Nanjing Lukou Airport and Hangzhou Xiaoshan Airport in the Yangtze river delta airport group as an example, the numerical simulation is carried out. The results show that when the comprehensive strength ratio of the two airports is greater than the demand of the corresponding airport in the hinterland cross region, the two airports achieve the competition equilibrium in the cross region of the radiation domain.This provides a theoretical analysis method for an airport to improve its competitiveness in a regional multi-airport system.