A new method is proposed for robust partial quadratic eigenvalue assignment problem (RPQEAP) with repeated prescribed eigenvalues. We first derive a result on the solution of partial quadratic eigenvalue assignment problem, which leads to the partial Schur form of the closed-loop system. Then by minimizing the normality departure of the partial Schur form of the closed-loop system, we assign the prescribed eigenvalues step by step such that the closed-loop system is as robust as possible. Our method allows the prescribed eigenvalues are repeated. Moreover, the proposed method does not use the unchanged eigenpairs of the open-loop system and avoids transforming the second-order control system to the first-order system. Numerical experiments show that the proposed method is efficient for solving the RPQEAP with repeated eigenvalues.