This paper proposes a simple modification of the Cuckoo Search called CS for a dynamic environment. In this paper, we consider a dynamic optimization problem where the global optimum can be cyclically changed depending on time. Our modified CS algorithm holds good candidates in order to effectively explore the search space near those candidates with an intensive local search. Our first experiment tests the prosed method on a set of static optimization problems, which aims at evaluating the potential performance of the proposed method. Then, we apply it to a dynamic optimization problem. Experimental results on the static problems show that the proposed method derives a better performance than the conventional method, which suggest the proposed method potentially has a good capability of finding a good solution. On the dynamic problem, the proposed method also performs well while the conventional method fails to find a better solution.