In view of the multi-attribute decision making problem with attribute values being three-parameter interval number and weights unknown, a new decision making approach based on nonlinear extension dependent degree is proposed. According to traditional extension simple dependent functions, it proposes a nonlinear extension dependent function for three-parameter interval number. Then, through an interval mapping transformation operator, the processes of computing dependent degree under different types of attributes are transformed to the simple and monotonous process under benefit-type attribute. The method can not only reflect decision uncertainty from risk preference of a decision maker by adjusting its attitude coefficients, but also express a nonlinear thinking model in the evaluation of people. Finally, an example is presented to illustrate the effectiveness and stability of the proposed method.