Layered superconductors have provided some interesting fields in condensed matter physics owing to the low dimensionality of their electronic states. For example, the high-Tc (high transition temperature) cuprates and the Fe-based superconductors possess a layered crystal structure composed of a stacking of spacer (blocking) layers and conduction (superconducting) layers, CuO2 planes or Fe-Anion layers. The spacer layers provide carriers to the conduction layers and induce exotic superconductivity. Recently, we have reported superconductivity in the novel BiS2-based layered compound Bi4O4S3. It was found that superconductivity of Bi4O4S3 originates from the BiS2 layers. The crystal structure is composed of a stacking of BiS2 superconducting layers and the spacer layers, which resembles those of high-Tc cuprate and the Fe-based superconductors. Here we report a discovery of a new type of BiS2-based layered superconductor LaO1-xFxBiS2, with a Tc as high as 10.6 K.