High- Tc superconducting fibers with highly oriented grain structure have been grown by means of Laser-Floating-Zone Growth(LFZG). A CW CO2 laser has been taken to produce a miniature controlled melting zone at 800-1100°C. The a-b planes of the grains are parallel to the fiber axis (along the growth direction), providing the ideal . condition for current conduction. The measured Tc is 110 K and Jc more than 5000 A/cm. The influence of growth technology and post growth heat treatment condition on the structure and the superconducting properties is also discussed.