We show an efficient pattern-matching algorithm for strings that are succinctly described in terms of straight-line programs, in which the constants are symbols and the only operation is the concatenation. In this paper, both text T and pattern P are given by straight-line programs T and P . The length of the text T (pattern P, resp.) may grow exponentially with respect to its description size ||T|| -- n (||P|| = m, resp.). We show a new combinatorial property concerning with the periodic occurrences of a pattern in a text. Based on this property, we develop an O(n2m2) time algorithm using O(nm) space, which outputs a compact representation of all occurrences of P in T. This is superior to the algorithm proposed by Karpinski et al., which runs in O((n + m)4 log (n + m)) time using O((n + m)3) space, and finds only one occurrence. Moreover, our algorithm is much simpler than theirs.