We propose a novel cloud-based precise positioning system that uses visual sensing data. Any mobile module with a vision sensor and wireless communication can be a client and can receive benefit from this system. When the client module takes a picture of an environment and uploads it to the server, it receives the shooting position with 6 degrees of freedom (DoFs) with an accuracy on the order of centimeters within a couple of seconds. The server maintains a map of the environment and localizes the uploaded picture in the map. The contributions of this paper are threefold. First, we develop a new visual localization method using a 3D wireframe map. The method proceeds in three steps: (i) the generation of an arbitrary perspective 2D image composed of line segments from a 3D wireframe map, (ii) the gradient dilation of a line segment image for effective image retrieval, (iii) pixelwise-AND-based image-similarity evaluation by parallel computing. Second, we build 3D CAD models of an actual building from a 2D design drawing and with manual measurements. Third, we experimentally evaluate our method using virtual sensing data.