Direction of Arrival (DOA) estimation is an important technique for speech perception and speaker localization, which has received much attention in recent years. However, most conventional methods concentrate on noisy environments, which leads to serious degradation of their performance in the presence of reverberation. To resolve this phenomenon, a novel approach based on reverberation weighting and noise error estimator by two microphones is proposed for robust DOA estimation in this paper. Firstly, the reverberations in received microphone signals are suppressed by late and early reverberation gains estimated by a spectral subtraction rule and the coherence of direct-arrival signals respectively. Then, the reverberation-suppressed signals are utilized to extract the time difference of arrival (TDOA) by the noise error estimator to reduce the affect of noise. At last, the final DOA is determined by the obtained TDOA combing with the geometry of the microphone array. The proposed method is evaluated in a simulated rectangular room with different levels of noise and reverberation, and experimental results validate that our method achieves favorable performance compared with traditional ones.