Satellite Internet of Things (S-IoT), which integrates satellite networks with IoT, is a new mobile Internet to provide services for social networks. However, affected by the dynamic changes of topology structure and node status, the efficient and secure forwarding of data packets in S-IoT is challenging. In view of the abovementioned problem, this paper proposes an adaptive routing strategy based on improved double Q-learning for S-IoT. First, the whole S-IoT is regarded as a reinforcement learning environment, and satellite nodes and ground nodes in S-IoT are both regarded as intelligent agents. Each node in the S-IoT maintains two Q tables, which are used for selecting the forwarding node and for evaluating the forwarding value, respectively. In addition, the next hop node of data packets is determined depending on the mixed Q value. Second, in order to optimize the Q value, this paper makes improvements on the mixed Q value, the reward value, and the discount factor, respectively, based on the congestion degree, the hop count, and the node status. Finally, we perform extensive simulations to evaluate the performance of this adaptive routing strategy in terms of delivery rate, average delay, and overhead ratio. Evaluation results demonstrate that the proposed strategy can achieve more efficient and secure routing in the highly dynamic environment compared with the state-of-the-art strategies.