We have theoretically designed and experimentally observed free-space propagation of topological singular lines of cylindrical vector optical fields with non-integer topological charges. The polarization singular lines are due to the orientation uncertainty of the polarization states, caused by non-integer topological charges. The results reveal that during propagation, evolution of the polarization singular lines results in the special intensity pattern, distribution of polarization states, and chains of polarization singularities. We have also proposed a method to generate triple straight and spiral singular lines, which may contribute to the research of complex optical fields.