This article presents the comprehensive framework for a hybrid-driven underwater vehicle-manipulator system (HD-UVMS) to grasp marine products on the seabed. The purpose of the proposed hybrid-driven propulsion system is to improve the swimming ability of the HD-UVMS by using thrusters and enhance the stability of its pose adjustment mechanism via two unique long fin propulsors. The control mode for the thrusters and long fin propulsors is based on a fuzzy logic control method. Subsequently, a lightweight manipulator is developed to grasp marine products. The open-closed angle and current controls for the gripper help to avoid damaging marine products. A vision system is installed to enable the HD-UVMS to gradually approach marine products with the aid of monocular vision and grasp them with the aid of binocular vision. A detailed method for monocular passive ranging and stereo matching, in accordance with real-time metrics, is elaborated. Finally, relevant experiments are conducted in an indoor pool and under real sea condition to assess the effectiveness of the proposed framework.