In the paper, the shape stability of single crystal fibers grown by laser heating float zone growth method is studied with zone melt growth theory. The relation of melting zone length (1) during steady-state crystal growth to the diameters of source rod (D) and fiber (d) is explained. It is indicated that the laser heated source stability and the homogeneity of source rod are the major factors influencing the fiber diameter fluctuation. The conclusion deduced from theory agrees with the experimental results.