With the rapid development of the civil aviation industry, the quantity of flights has significantly increased. However, how to take good advantage of airplanes becomes a problem, and this problem is the flight connection problem. Some flights can use one plane, while some flights cannot. Appropriate allocation of airplanes can maximize the profit and save the time. This paper chooses 12 pairs in Indira Gandhi National Airport. Then, it draws a bipartite graph and builds a zero-one integer programming model. Next, it introduces the constraints subject to the regulations in the aviation industry. Employing the branch and bound method is infeasible at the first time, which means some flights cannot be connected. After altering the constraints, an optimal solution is obtained, ensuring that the number of aircraft is minimal and the airport operates well at the same time. This flight connecting model can also be applied in other circumstances.