<p>To eliminate the limitations of the Shannon entropy as the risk attribute in decisions under risk, a novel model of decision-making under risk is proposed based on the expected utility and the cumulative residual entropy. This model can explain the preference between risky prospects by two attributes, that is, the expected utility and the cumulative residual entropy. The proposed model of decision-making under risk has rich theoretical features, and it also shares attractive properties of the expected utility and the cumulative residual entropy. The applicability and effectiveness of the proposed model are verified by interpreting several decision-making phenomena effectively. Through comparison and analysis, it is also shown that the proposed model of decision-making under risk has many advantages over the existing models constructed by the combination of expected utility and other risk attributes, such as the Shannon entropy and the variance. Finally, an application of the proposed model is conducted to characterize the investor’s preferences and then select the stocks in the FTSE China A50 Index with a higher preference for constructions of optimal portfolios. The empirical results reveal that without changing the main properties of optimal portfolios, the number of selected stocks can be reduced to 25% through the proposed model of decision-making under risk.</p>