An urban operation of unmanned aerial vehicles (UAVs) demands a high level of autonomy for tasks presented in a cluttered environment. While fixed-wing UAVs are well suited for long-endurance missions at a high altitude, enabling them to navigate inside an urban area brings another level of challenges. Their inability to hover and low agility in motion cause more difficulties on finding a feasible path to move safely in a compact region, and the limited payload allows only low-grade sensors for state estimation and control. We address the problem of achieving vision-based autonomous navigation for a small fixed-wing in an urban area with contributions to the following several key topics. Firstly, for robust attitude estimation during dynamic maneuvering, we take advantage of the line regularity in an urban scene, which features vertical and horizontal edges of man-made structures. The sensor fusion with gravity-related line segments and gyroscopes in a Kalman filter can provide driftless and realtime attitude for ight stabilization. Secondly, as a prerequisite to sensor fusion, we present a convenient self-calibration scheme based on the factorization method. Natural references such as gravity, vertical edges, and distant scene points, available in urban fields, are sufficient to find intrinsic and extrinsic parameters of inertial and vision sensors. Lastly, to generate a dynamically feasible motion plan, we propose a discrete planning method that encodes a path into interconnections of finite trim states, which allow a significant dimension reduction of a search space and result in naturally implementable paths integrated with ight controllers. The most probable path to reach a target is computed by the Markov Decision Process with motion uncertainty due to wind, and a minimum target observation time is imposed on the final motion plan to consider a camera's limited field-of-view. In this thesis, the effectiveness of our vision-based navigation system is demonstrated by what we call an "air slalom" task in which the UAV must autonomously search and localize multiple gates, and pass through them sequentially. Experiment results with a 1m wing-span airplane show essential navigation capabilities demanded in urban operations such as maneuvering passageways between buildings.