Satellite communications has been regarded as an indispensable technology for future mobile networks to provide extremely high data rates, ultra-reliability, and ubiquitous coverage. However, the high dynamics caused by the fast movement of low-earth-orbit (LEO) satellites bring huge challenges in designing and optimizing satellite communication systems. Especially, admission control, deciding which users with diversified service requirements are allowed to access the network with limited resources, is of paramount importance to improve network resource utilization and meet the service quality requirements of users. In this paper, we propose a dynamic channel reservation strategy based on the Actor-Critic algorithm (AC-DCRS) to perform intelligent admission control in satellite networks. By carefully designing the long-term reward function and dynamically adjusting the reserved channel threshold, AC-DCRS reaches a long-run optimal access policy for both new calls and handover calls with different service priorities. Numerical results show that our proposed AC-DCRS outperforms traditional channel reservation strategies in terms of overall access failure probability, the average call success rate, and channel utilization under various dynamic traffic conditions.