A problem of dynamic risk decision-making with interval grey numbers and unknown attributes’ weights is studied. A method based on the cumulative prospect theory and grey target thoughts is proposed. Firstly, the distance measure and the ranking method for interval numbers are defined, respectively. Dynamic prospect matrixes are calculated by using the average value of all attributes’ values as the preference point. Then the static prospect matrix is aggregated by dynamic prospect matrixes via WAA operator. Furthermore, every attribute’s weight is obtained from a programming model based on the maximum entropy. In addition, the new positive and negative ellipsoid grey target models are constructed, and distances between every project and positive, negative target-center are computed, which are aggregated to comprehensive ones to rank projects. Finally, numerical results show that the proposed method is more consistent with the human psychological behavior compared with other approaches.