The paper studies the coordination of main manufacturer-suppliers supply chain under the background of weak main manufacturers in the initial period of China's large passenger aircrafts. Under the competition of multiple suppliers and manufacturers, the main manufacturer selects a strong supplier to build cooperation, designs a relational contract based on specific asset investment, and allocates the benefits derived from the cooperation linearly to incentive the strong supplier to establish cooperation with the main manufacturer. We illustrate the equilibrium decision of the competition among multiple suppliers and manufacturers under different scenarios, and then analyze the dominance and the evolution of the relational contract from different aspects. The research shows that the cooperation relationship would be established if the relational contract can be self-executing as well as the profit of weak main manufacturer and strong supplier are as expected. The optimal quantity and price are determined by the competition when the strong supplier refuses the relational contract or there is no contract coordination. The relational contract is superior comparing with perfect competition, which can coordinate the weak main manufacturer and the relatively strong supplier to establish the cooperation relationship, and improve their profitability and competitiveness.