The problems to compute the distances or similarities of multiple strings have been vigorously studied in such diverse fields as pattern matching, web searching, bioinformatics, computer security, etc. One well-known method to compare multiple strings in the given set is finding a consensus string which is a representative of the given set. There are two objective functions that are frequently used to find a consensus string, one is the radius and the other is the consensus error. The radius of a string x with respect to a set S of strings is the smallest number r such that the distance between the string x and each string in S is at most r. A consensus string based on radius is a string that minimizes the radius with respect to a given set. The consensus error of a string with respect to a given set S is the sum of the distances between x and all the strings in S. A consensus string of S based on consensus error is a string that minimizes the consensus error with respect to S. In this paper, we show that the problem of finding a consensus string based on radius is NP-complete when the distance function is a metric.