Metric spaces are generalized by many scholars. Recently, Khatami and Mirzavaziri use a mapping called t-definer to popularize the triangle inequality and give a generalization of the notion of a metric, which is called a ⋆-metric. In this paper, we prove that every ⋆-metric space is metrizable. Also, we study the total boundedness and completeness of ⋆-metric spaces.