The crack assessment for the boilers or steam-turbines of conventional power plants has been carried out by means of conventional fracture mechanics. Here, the cracks are large enough in comparison with the grains in the material, so that the inhomogeneity due to the microstructure can be ignored. However, in the gas-turbine blade, the size of grain is relatively larger than that in conventional plant components, and the crack propagation property may be affected by the local grain configuration. Here, in order to clarify the crack propagation property of an anisotropic material (Ni-based directionally solidified superalloy for the gas-turbine blades), high temperature fatigue tests are conducted using longitudinal loading specimens with a crack (L-specimens) and transverse loading ones (T-specimens). The crack propagation rate is roughly correlated well with the effective stress intensity factor range regardless of the propagation direction (specimens L and T), the stress range, and the stress ratio. In detail, however, the crack propagation rate shows eminent fluctuation particularly in the T-specimens. It is about 5 times faster than the average at most. The feature of fracture surface can be classified into 4-types where 3 of them are transgranular and the other is intergranular. In the former, though the crack is along {100} or {110} planes in the macroscopic scale, it threads through {111} or {100} planes in the microscopic scale. The crack propagation is eminently accelerated in the intergranular region while the deceleration is caused by the crack-branching.