The measuring system of fiber position of LAMOST (Large Area Multi-Object Fiber Spectroscope Telescope) is introduced in this paper. A method of photometric gravity's center is discussed. A laboratorial system for measuring position of a few of fibers in a small scale has been finished. The results of the experiment are satisfactory. Based on the experience of laboratorial experiments, we are now designing the measuring system of fiber position of LAMOST. A conceptual design is described in this paper.