The portable three-dimensional vision coordinate measuring system, which consists of a light pen, a CCD camera and a laptop computer, can be widely applied in most coordinate measuring fields especially on the industrial spots. On the light pen there are at least three point-shaped light sources (LEDs) acting as the measured control characteristic points and a touch trigger probe with a spherical stylus which is used to contact the point to be measured. The most important character of this system is that three light sources and the probe stylus are aligned in one line with known positions. In building and studying this measuring system, how to construct the system’s mathematical model is the most key problem called perspective of three-collinear-points problem, which is a particular case of perspective of three-points problem (P3P). On the basis of P3P and spatial analytical geometry theory, the system’s mathematical model is established in this paper. What’s more, it is verified that perspective of three-collinear-points problem has a unique solution. And the analytical equations of the measured point’s coordinates are derived by using the system’s mathematical model and the restrict condition that three light sources and the probe stylus are aligned in one line. Finally, the effectiveness of the mathematical model is confirmed by experiments.