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The iterative closest point (ICP) algorithm is fast and accurate for rigid point set registration, but it works badly when handling noisy data or point clouds with outliers. This paper instead proposes a novel method based on the ICP algorithm to deal with this problem. Firstly, correntropy is introduced into the rigid registration problem which could handle noises and outliers well, and then a new energy function based on maximum correntropy criterion is proposed. After that, a new ICP algorithm based on correntropy is proposed, which performs well in dealing with rigid registration with noises and outliers. This new algorithm converges monotonically from any given parameters, which is similar to the ICP algorithm. Experimental results demonstrate its accuracy and robustness compared with the traditional ICP algorithm.