Summary: In most earlier works of differential game problems, which are based solely on crisp mathematics, it is generally assumed that all information obtained by each player is perfect; thus the games are treated with full information. In many practical situations, the information obtained by any player may contain some sort of uncertainties, which are usually difficult to characterize either deterministically or stochastically. We treat such uncertain information as fuzzy information and consider a differential game problem with fuzzy information as a fuzzy differential game problem. In this paper, we consider the fuzzy differential game of guarding a movable territory. In a general problem of guarding a territory, key concepts are the favorable region of the invader and the boundary curve. For simplicity, the movable territory is assumed to be a circle in this paper. We will show that when the center of the territory is located outside the favorable region of the invader, the value of the game exists; otherwise the value does not exist. A fuzzy control strategy is proposed and some computer simulations are provided in this paper.