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Despite the prevalence of robotic manipulation tasks in various real-world applications of different requirements and needs, there has been a lack of focus on enhancing the adaptability of robotic grasping systems. Most of the current literature constructs models around a single gripper, succumbing to a trade-off between gripper complexity and generalizability. Adapting such models pre-trained on one type of gripper to another to work around the trade-off is inefficient and not scalable, as it would require tremendous effort and computational cost to generate new datasets and relearn the grasping task. In this letter, we propose a novel hybrid architecture for robot grasping that efficiently learns to adapt to different gripper designs. Our approach involves a three step process that first obtains a rough grasp pose prediction from a parallel gripper model, then predicts an adaptive action using a convolutional neural network, and finally refines the predicted action with reinforcement learning. The proposed method shows significant improvements in grasping performance compared to existing methods for both generated datasets and real-world scenarios, presenting a promising direction for improving the adaptability and flexibility of robotic manipulation systems.