A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library. The fluid motion is solved by Peskin’s diffuse-interface immersed boundary （IB） method， which is attractive for simulating moving-boundary flows with large deformations. The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution. The dynamic response of the parachute is solved with the finite element approach. The canopy and cables of the parachute system are modeled with the hyperelastic material. A tether force is introduced to impose rigidity constraints for the parachute system. The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate. Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation.