We propose a novel real-time direct monocular visual odometry for omnidirectional cameras. Our method extends direct sparse odometry (DSO) by using the unified omnidirectional model as a projection function, which can be applied to fisheye cameras with a field-of-view (FoV) well above 180 degrees. This formulation allows for using the full area of the input image even with strong distortion, while most existing visual odometry methods can only use a rectified and cropped part of it. Model parameters within an active keyframe window are jointly optimized, including the intrinsic/extrinsic camera parameters, 3D position of points, and affine brightness parameters. Thanks to the wide FoV, image overlap between frames becomes bigger and points are more spatially distributed. Our results demonstrate that our method provides increased accuracy and robustness over state-of-the-art visual odometry algorithms.