The aim of this paper is to design a new type of grasping and perching unmanned aerial vehicle (UAV), called Flexbee, which features a soft vector-propulsion nozzle (SVPN). Compared to previous UAVs, Flexbee integrates flight, grasping, and perching functionalities into the four SVPNs. This integration offers advantages including decoupled position and attitude control, high structural reuse, and strong adaptability strong adaptability for grasping and perching. A dynamics model of Flexbee has been developed, and the nonlinear coupling issue of the moment has been resolved through linearization of the equivalent moment model. A hierarchical control strategy was used to design controllers for the two operational modes of Flexbee. Finally, flight, grasping, and perching experiments were conducted to validate Flexbee's kinematic capabilities and the effectiveness of the control strategy.