The solution of the inverse quadratic programming problem with inequality constraint was studied. Firstly, the form of inverse problem corresponding to this kind of quadratic programming was written, and then the inverse problem was transformed into an optimization problem with separable objective functions. After the constraints were written in the form of KKT conditions, the inverse problem was equivalent to an equality-constrained optimization problem. Based on above transformation, the alternating direction method of multipliers (ADMM) was considered for iteration. On this basis, the homotopy idea was applied to the subproblems of each iteration of our algorithm, so as to avoid the sensitivity of the selection of proximal operators and ensure the convergence speed of the algorithm. For the subproblems, the successive over-relaxation method was used to solve them, and the convergence of the algorithm was obtained. Finally, comparing the proposed method with SDPT3 and Sedumi, the results show that our algorithm is superior to the above two methods both in speed and efficiency.