Target direction-of-arrival (DOA) estimation is often difficult in the presence of strong interference-especially when the target DOA is very close to the interference DOA-since the strong interference signal can mask the weak target signal and make the DOA estimation hard. To address this problem, an efficient sparse method for DOA estimation is proposed in this paper, in which the effect of strong interference on the target DOA estimation is significantly reduced. An on-grid version of the grid evolution technique is then developed to nonuniformly refine the grid, thereby reducing the computational complexity while retaining reasonable accuracy. Numerical simulations and experimental results demonstrate that, compared to state-of-art methods, the proposed method achieves higher efficiency and better DOA estimation performance in the presence of strong interference.