The effect of the grain-boundary microstructures on the creep-rupture properties and the initiation and growth of the grain-boundary cracks was investigated using four kinds of specimen of various grain-boundary microstructures in the cobalt-base HS-21 alloy at 1089 K in air. Both the rupture strength and the creep ductility increased with increasing mean value of the fractal dimension of the grain boundaries, D-gb. The strain to crack initiation was largest in the specimen of the highest D-gb value (1.241), while the strain was much the same in the specimens of the D-gb value less than 1.162. This was explained by the local variation in the grain-boundary microstructures in these specimens. The mean value of the fractal dimension of the grain-boundary fracture, D-f, was close to the value of D-gb, although the value of D-f was a little higher than that of D-gb in the specimens of the lower D-gb values. The fracture appearance changed from a brittle grain-boundary fracture to a ductile one with increasing values of D-gb and D-f. The crack-growth rate is the surface-notched specimens decreased with increasing value of D-gb. The threshold stress intensity factor for crack growth was higher in the specimens with the higher D-gb values.