The classical algorithms in DOA (Direction Of Arrival) estimation endure two obvious drawbacks that they are invalid when faced with the time-varying signals and difficult to be implemented in hardware. In this paper, we propose that Locally Competitive Algorithm (LCA) be applied to estimate the time-varying signals' DOA innovatively. In order to solve the l1-minimization problems rapidly and efficiently, LCA bases on the continuous-time dynamical system which uses the principles of threshold to induce the local competitions. According to a series of nonlinear ordinary differential equations, LCA can be expressed by the simple analog hardware, which is distinctly different from the classical algorithms. We show that LCA is capable of tracking the change of time-varying signals effectively.Index Terms-DOA estimation, dynamic system, LCA, l1-minimization problem