The visual based indoor positioning solution is challenging to provide high-precision positioning in areas with unobtrusive features. Most current solutions refer to low precision, expensive, or priori training. The ceiling distributed on the same plane is arranged regularly and widespread in structured indoors. We propose a new monocular vision simultaneous localization and mapping (NMV SLAM) for high-precision indoor positioning. First, image morphology technology is adopted to extract the ceiling corner accurately. Second, the geometric solution based on the priori map composed of ceiling realizes global positioning and makes up for the deficiency of time-consuming nonlinear optimization. Experiments show that the root mean square error (RMSE) of position measured by the proposed NMV SLAM is less than 5.43 mm in a room with an entire ceiling. Moreover, the proposed NMV SLAM processes an average of 30.61 frames in one second on an i5-9400F CPU processor.