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Normed linear spaces play an important role in pure and applied mathematics. In particular, Banach spaces are useful tools for problem-solving in computational science. Mathematicians have showed the geometric structureof Banach spaces since the introduction of uniform convexity by J. A. Clarkson. B. Beauzamy presented a characterization of uniform convexity of Banach spaces. This result was an important property to elucidate the geometric struc ture of Banach spaces. It contributed to solve various optimization problems.On the other hand, H. Busemann constructed a theory of non-positive curvature of metric spaces. Using this theory, B. H. Bowditch introduced nonpositive curvature spaces called Busemann spaces. Busemann spaces are more general than strictly convex Banach spaces. In recent years, Busemann spaces have attracted attention for their use in computational science. Against this background, the study of the geometric structure of Busemann spaces is valuable of pure and applied mathematics.In this paper, I discuss uniform convexity of complete Busemann spaces. As a main result, I prove a characterization of uniform convexity of Busemann spaces. This is a generalization of the characterization of uniform convexity of Banach spaces given by Beauzamy.