Automatic laparoscope motion control is fundamentally important for surgeons to efficiently perform operations. However, its traditional control methods based on tool tracking without considering information hidden in surgical scenes are not intelligent enough, while the latest supervised imitation learning (IL)-based methods require expensive sensor data and suffer from distribution mismatch issues caused by limited demonstrations. In this paper, we propose a novel Imitation Learning framework for Laparoscope Control (ILLC) with reinforcement learning (RL), which can efficiently learn the control policy from limited surgical video clips. Specially, we first extract surgical laparoscope trajectories from unlabeled videos as the demonstrations and reconstruct the corresponding surgical scenes. To fully learn from limited motion trajectory demonstrations, we propose Shape Preserving Trajectory Augmentation (SPTA) to augment these data, and build a simulation environment that supports parallel RGB-D rendering to reinforce the RL policy for interacting with the environment efficiently. With adversarial training for IL, we obtain the laparoscope control policy based on the generated rollouts and surgical demonstrations. Extensive experiments are conducted in unseen reconstructed surgical scenes, and our method outperforms the previous IL methods, which proves the feasibility of our unified learning-based framework for laparoscope control.