In this paper, we propose a new method to design an annihilating filter (AF) for direction-of-arrival (DOA) estimation of multiple snapshots within an uniform linear array. To evaluate the proposed method, we firstly design a DOA estimation using multiple signal classification (MUSIC) algorithm, referred to as the MUSIC baseline. We then compare the proposed method with the MUSIC baseline in two environmental noise conditions: Only white noise, or both white noise and diffusion. The experimental results highlight two main contributions; the first is to modify conventional MUSIC algorithm for adapting different noise conditions, and the second is to propose an AF-based method that shows competitive accuracy of arrival angles detected and low complexity compared with the MUSIC baseline.