Abstract:In this paper, we introduce the uniform continuity of functional on a metric space and the test function of a uniform continuity.The character of test function and the relation between the test function and the uniform continuity are studied.Using the test function, we obtain a necessary and sufficient condition of determining the uniform continuity of functional on a metric space or a sub-normed Z-linear space. In this case, it is simple to determine the uniform continuity of functional.