The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method for nuclear norm constrained problems. The goal is to generate descent steps that lead to rank decreases, maintaining low-rank solu- tions throughout the algorithm. Moreover, the op- timization problems are constrained to ensure that the rank-drop step is also feasible and can be read- ily incorporated into a projection-free minimization method, e.g., Frank-Wolfe. We demonstrate that by incorporating rank-drop steps into the Frank-Wolfe algorithm, the rank of the solution is greatly re- duced compared to the original Frank-Wolfe or its common variants.