Multi-attribute decision problems with uncertainty largely exist in the real world, it is very necessary to solve these problems. The paper proposes a grey correlation method based on maximizing deviation to solve the multiple attribute decision-making problems under risk in which the weight is unknown and attribute values are interval numbers. In the grey correlation method, according to different attributes and their natural states, the decision matrix is normalized and ideal/ negative ideal solutions are also determined respectively; then, maximizing deviation method is used to determine the weights of attributes, and grey correlation method is used to rank the alternatives by using relative closeness coefficients. The computational results from an illustrative example have shown that the proposed approach is feasible and effective for the multiple attribute decision making problems under risk.