This paper proposes a new DOA (direction of arrival) estimation method based on circular microphone array. For an arbitrary number of microphones, it is analytically shown that DOA estimation reduces to an efficient non-linear optimization problem. Simulation results demonstrate that deviation of the estimation error for 20 and 10 dB SNR is smaller than 0.7 degree which is comparable to high resolution DOA estimation methods. A larger number of microphones provide a more omni- directional spatial resolution.