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This paper proposes a vision-based obstacle avoidance strategy in a dynamic environment for a fixed-wing unmanned aerial vehicle (UAV). In order to apply a nonlinear model predictive control (NMPC) framework to image-based visual servoing (IBVS), a dynamic model from UAV control input to image features is derived. From this dynamics, a visual information-based obstacle avoidance strategy in an unknown environment is proposed. When a vision system is employed on a UAV, it is easy to lose visibility of the target in the image plane due to its maneuvering. To address this issue, a visibility constraint is considered in the NMPC framework. The advantage of the proposed method is that the constraints (e.g., visibility maintaining, actuator saturation) can be modeled and solved in a unified framework. Numerical simulations on a UAV model show satisfactory results in reference tracking and obstacle avoidance maneuvers with the constraints.