In this paper we study the problem of deciding whether a given compressed string contains a square . A string x is called a square if x = zz and z = u^k implies k = 1 and u = z . A string w is said to be square-free if no substrings of w are squares. However, very little is known for testing square-freeness of a given compressed string . In this paper, we give an O( max(n^2, n log^2 N)) -time O(n^2) -space solution to test square-freeness of a given compressed string, where n and N are the size of a given compressed string and the corresponding decompressed string, respectively. Our input strings are compressed by balanced straight line program ( BSLP ). We remark that BSLP has exponential compression, that is, N = O(2^n) . Hence no decompress-then-test approaches can be better than our method in the worst case.