The B_*-axicm is introduced by professor Li Xiaochuan. Many studies on the B_*-axiom are made by him. Especially, he proves that if (X,d) is a metric space, d and d' are topology-equivalent, then in (X,d) B_*-axiom is true (?)(X,d') is a separable space. In this paper, the famous Nagata-Smirnov metrization theorem is employed to a metric space in which B_*-axiom is nontrue to make a one-point extension, and the extensional space is proved to be metrizable space.