Oilfield pipes with out-of-tolerance internal thread can lead to failures, so the internal thread geometric parameters need to be measured. To tackle the problem of the low efficiency, poor accuracy, easy wear, and poor accessibility of existing methods, a single-lens multi-mirror laser stereo vision-based system for measuring geometric parameters of the internal thread is proposed, which allows the measurement of three parameters in one setup by completely reproducing the three-dimensional (3D) tooth profiles of the internal thread. In the system design, to overcome the incomplete representation of imaging parameters caused by insufficient consideration of dimensions and structural parameters of the existing models, an explicit 3D optical path model without a reflecting prism is first proposed. Then, considering the intervention of the reflecting prism, a calculation model for the suitable prism size and the final imaging parameters of the vision system is proposed, which ensures the measurement accessibility and accuracy by solving the problem that the existing system design only depends on experience without theoretical basis. Finally, based on the American Petroleum Institute standard, internal thread geometric parameters are obtained from the vision-reconstructed 3D tooth profiles. According to the optimized structural parameters, a vision system is built for measuring the internal thread geometric parameters of two types of oilfield pipes. Accuracy verification and typical internal thread measurement results show that the average measurement errors of the vision system proposed for the pitch, taper, and tooth height are 0.0051 mm, 0.6055 mm/m, and 0.0071 mm, respectively. Combined with the vision measurement time of 0.5 s for the three parameters, the above results comprehensively verify the high accuracy and high efficiency of the vision-based system.