Calibration is a crucial step in fringe projection profilometry, which establishes the relationship between unwrapped phase and (FPP) three-dimensional (3-D) shape data (X,Y,h). For an arbitrarily arranged FPP system, a simple geometrical model and mathematical descriptions of the relationships among phase, height distribution, and transverse coordinate are presented. Based on this, a flexible global calibration method is presented to reconstruct 3-D shape by just using a checkerboard with known separation and alternating white and blue. The calibration board is placed at several random positions to determine the relationship between phase and height, and the relationship between pixel position and X, Y coordinates. To get high accuracy, distortion for each pixel is considered. The validity, flexibility, and practicality of this system and calibration technique are verified by experiments.