Game theory is commonly used in competitive situations because of its significance in decisionmaking. Different types of fuzzy sets can handle uncertainty in matrix games. Neutrosophic set theory plays a vital role in analyzing complexity, ambiguity, incompleteness, and inconsistency in real-world problems. This study develops a novel approach to solve neutrosophic matrix games using linear programming problems with single-valued triangular neutrosophic numbers as pay-offs. This paper establishes some theoretical aspects of game theory in a neutrosophic environment. A numerical example verifies the theoretical results using the traditional simplex approach to achieve the strategy and value of the game. The proposed work is useful to model and solve conflict situations in decision-making problems with partial knowledge as data in a simple manner.