Mathematic model of detector is the basis of precise detection. A complete mathematical model of four-quadrant photodetector has been built by analyzing the ray-path of photodetector in this paper. In the model, the effects of the offset of fixed position of four-quadrant photodetector happened when photodetector was being installed, the distance between photosurface and focus of photodetector, and other architecture parameters of photodetector on the conversion from light to electricity are considered. On the basis of building the models of photodetector in three particular positions, viz. pitching departure position, orientation departure position, rolling departure position, the common relation expressions between light signals, the offset of mounted position of four-quadrant photodetector, the distance between photosurface and focus of photodetector, and the electricity signal, the output signal are given. Comparing the waveforms of the output signals of the mathematic model of the photodetector and that of practical output signals of detector, it is found that the waveforms of model resembled that of detector in appearance. Comparing the feature parameters of the output signals of model and that of practical output signals, viz. the slope and intercept of tangent on crossover point of outputs, it is found that the differences are less than 0.01. So the relation between the inputs and outputs of the mathematical model was consistent with that between the inputs and outputs of the detector, and the model can be used in practical detection. And a foundation for the profound research and application of photodetector, detection without experiment samples is founded.