A new method based on a telecentric lens and curved screen is proposed to measure a discontinuous mirror's three-dimensional (3D) shape. This technique increases the imaging range of mirrors having large curvature and improves the measurement accuracy of 3D data. First, a display screen shows sinusoidal fringe patterns, and a camera records the sinusoidal fringe images reflected through the plane reference mirror and the measured mirror. Second, the corresponding phase distribution is obtained using the four-step phase shift method and the optimal three fringe selection method. The phase change modulated by the object surface of the measured mirror is obtained by comparison to the plane reference mirror. Furthermore, according to the established mathematical model, the relationship between phase and depth is deduced, and the system parameters are calibrated. Finally, measurements are taken to verify the accuracy and effectiveness of the proposed method using an artificial mirror step with large curvature and a discontinuous mirror.