Recently, there has been a surge of interest in incorporating fairness aspects into classical clustering problems. In this paper, we consider adding fairness constraints to k-center clustering. We use points with different colors to present individuals in distinct groups, the difference with the classic k- center clustering is that we try to constrain the number of centers selected from each group so that we can achieve the goal to guarantee the fairness. To solve this problem, Kleindessner et al. proposed a (5 + ϵ)-approximation algorithm in 2019. So far, the best algorithm to solve this problem is proposed by Jones et al., whose approximation ratio reached 3. The main contribution of this paper is: for fair k-center clustering, we propose a key set with special property and prove that there exists a structure for 2-approximation solution when the data set is divided into two groups.