Graphical bandit is an important model for sequential decision making under uncertainty and has been applied in various real-world scenarios such as social network, electronic commerce, and recommendation system. Existing work on graphical bandits only investigates how to identify the best arm rapidly so as to minimize the cumulative regret while ignoring the privacy protection issue arising in many real-world applications. To overcome this deficiency, a differentially private algorithm is proposed, termed as graph-based arm elimination with differential privacy (GAP), for graphical bandits. On the one hand, GAP updates the arm selection strategy based on empirical mean rewards of arms in an epoch manner. The empirical mean rewards are perturbed by Laplace noise, which makes it hard for malicious attackers to infer rewards of arms from the output of the algorithm, and thus protects the privacy. On the other hand, in each epoch, GAP carefully constructs an independent set of the feedback graph and only explores arms in the independent set, which effectively utilize the information in the graph feedback. It is proved that GAP is differential private and its regret bound matches the theoretical lower bound. Experimental results on synthetic datasets demonstrate that GAP can effectively protect the privacy and achieve cumulative regret comparable to that of existing non-private graphical bandits algorithm.