c-axis micro-bridges of La 2-x Sr x CuO 4 ( LSCO ) single crystals were fabricated by the focused-ion-beam (FIB) etching method. Small rectangular LSCO pieces were fabricated by cutting and grinding single crystals of underdoped LSCO of x=0.09. The size of LSCO single crystals between electrodes was cut to 20×40μm2 in ab-plane by using the FIB etching method. Superconductor-insulator-superconductor (SIS) like-branch structures on I-V curves of the LSCO stacks were observed for the first time. The branch structures exhibited voltage jumps of several tens mV in the range of from 1.7 K to 5 K with temperature dependence. When the temperature is changed from 5 K to 1.7 K , the critical current and the next branch split into a few of small voltage jumps with the intervals of several mV in the range of from 0.1 mV and 2.0 mV .