This article proposes a linear programming model based on an improved score function to solve interval-valued intuitionistic fuzzy multicriteria decision-making problems. In this decision-making process, the score matrix of the interval-valued intuitionistic fuzzy decision matrix can be constructed by the score function. We solve the linear programming model to determine the optimal criteria weights and then utilize the obtained criteria weights and the weighted score function as the suitability function of each alternative to rank the alternatives and select the most desirable one(s). Finally, an illustrative example for engineering investment alternatives demonstrates the effectiveness of the decision-making method.