Since liquid crystal display (LCD) screen locates outside of the camera’s field of view in fringe-reflection photogrammetry, fringes displayed on LCD screen are obtained through specular reflection by a fixed camera. Thus, the pose calibration between camera and LCD screen is one of the main challenges in fringe-reflection photogrammetry. A markerless planar mirror is used to reflect the LCD screen more than three times, and the fringes are mapped into the fixed camera. The geometrical calibration can be accomplished by estimating the pose between the camera and virtual image of fringes. With the help of the relation between their pose, incidence and reflection ray can be unified in the camera frame, forward triangulation intersection can be operated in the camera frame to measure 3D coordinate of specular surface. In the final optimization, constraint bundle adjustment is operated to refine simultaneously the camera intrinsic parameters including distortion coefficients, estimated geometrical pose between LCD screen and camera, 3D coordinate of specular surface, with the help of absolute phase collinear constraint. Results of simulations and experiments demonstrate that the pose calibration with planar mirror reflection is simple, feasible and constraint bundle adjustment can enhance the three-dimensional coordinate measurement accuracy in fringe-reflection photogrammetry.