The tolerance capability against ATWS for the FBR core with metallic fuel can be improved by employing a fuel with high thermal conductivity (HTC fuel) instead of the conventional metallic fuel, U-Pu-Zr. To investigate the self-controllability for the HTC-fueled core with U-Pu-Al alloy fuel, having one order of magnitude higher thermal conductivity than that of the U-Pu-Zr, the core employing the U-Pu-Al fuel was evaluated against ULOF and UTOP. Based on the systematic calculation, it was found that the larger temperature margin between the steady state and ULOF/UTOP conditions caused the excellent tolerance capability against ULOF and UTOP for the HTC-fueled core compared with that for the Zralloy-fueled core. Also, the conditions of the core reactivity coefficients required for neither fuel melting nor coolant boiling were investigated by using a ''self-controllability map'' consisting of effective fuel and coolant reactivities. As a result, the self-controllable region was found to be expanded especially for UTOP in the case of the HTC-fueled core.