In order to improve the measurement speed and accuracy of fringe projection three-dimensional (3D) measurement system, an approved phase-to-height mapping model is proposed. By building a virtual camera coordinate system and analyzing the conversion relation of fringe patterns between projector coordinate system and camera coordinate system, a one-to-one mapping relationship from phase to height in the camera corrected system is built and the lens distortion of the camera is included in the mapping model. Due to its simple expression, this model is suited for combining with look-up-table (LUT) method. With LUT method, this model can be used in high speed measurement because of its low algorithm complexity. Meanwhile, a calibration method for this model is proposed, and back-projection process is used to optimize the parameters of the camera in calibration process. The calibration method is easy to operate and no reference plane is needed. Also, the relative postures of the camera and the projector in fringe projection system can be arbitrarily arranged. Experimental results indicate that the proposed mapping model and its calibration method can achieve 3D measurement rapidly and accurately.