We fabricated resistive superconducting fault current limiters based on YB $a_{2}$/C $u_{3}$/ $O_{7}$ thin films and investigated their quench propagation characteristics. The YB $a_{2}$/C $u_{3}$/ $O_{7}$ films was coated with a gold layer and patterned into 1 mm wide meander lines by photolithography. The quench was concluded to start locally and propagates until completed. The quench propagation characteristics were explained based on the heat transfer within the film as well as between the film and the surrounding liquid nitrogen. The quench completion time depended strongly on potential fault current amplitude and not significantly on fault angle which indicates that the quench propagation speed is affected more by heat dissipation rate than by fault current increase rate. The quench completion time was 1 msec at the fault current of 65 $A_{peak/{ak}}$.