This work proposes a new neutron absorber, Cu-B composites, with excellent thermal conductivity and good neutron absorbing capability. Mixtures of elemental Cu and B powders with the B contents varying between 10 and 40 at.-% were consolidated into round bars by hot extrusion. The addition of B significantly refined the grain structure, which is related to the suppression of dynamic recrystallisation during hot extrusion and extended recovery during subsequent annealing. Such fine-grained structure in Cu-B composites together with dispersion hardening by B particles contributed to the higher hardness of Cu-B composites. The thermal conductivity of Cu-B composites, being roughly two times higher than that of Al-B4C MMC, decreases with increasing the B contents, which is mainly due to higher volume fraction B particles with lower thermal conductivity, and partly to texture randomisation and refined grain structure in the Cu-B composites.