To analyze the supersonic opening performance of the parachute in Mars reentry environment, the coupling dynamic models between compressible fluid and flexible structure of parachute were solved on the basis of the arbitrary Euler-Lagrange penalty function method and the multi-material arbitrary Lagrange Euler algorithm. The evolution of 3D shape of DGB(disk gap band) parachute during supersonic inflation was simulated, and the structural dynamic behaviors of canopy fabric were predicted. The drag area and coefficients were compared with the wind tunnel data, and the inflation performance of parachute and the influence of fore-body were analyzed. Finally, the wake of unsteady fluid and distribution of shock wave around supersonic parachute were investigated. The results show that: the DGB parachute is well inflated without serious collapse; as the increase of Mach numbers, the drag coefficients gradually decrease, along with the increase of the inflation time, which brings into correspondence with the test results, and proves the validity of the proposed method.