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Accurate hand-eye calibration is a very significant task in robotics. Many algorithms employ Least Square Estimation (LSE) and global nonlinear optimization to deal with this problem. LSE can lead to low calibration precision when gross errors occur. On the other hand, global nonlinear optimization strategy is easy to converge because of the influence of gross error. Different from the existing approaches, an error distribution estimation based weighted LSE is proposed for the robot hand-eye calibration task. Firstly, transformation matrix is computed by traditional LSE. Error distribution is estimated and the data is weighted according to the density estimation. Then the fine result can be conducted based on the weighted data. Lastly, iteration scheme is proposed to further improve the calibration accuracy. To evaluate the proposed method, an experiment was designed and the test result demonstrates the robustness of the proposed approach.