As a burnable poison element, boron (B) has been successfully added into the AlNbMoZr based refractory high-entropy alloy (RHEA) via arc melting method, thus a novel high strength nuclear RHEA material with neutron toxic properties was developed. Hence, the alloy was subjected to irradiation of Kr ions of 4 MeV intensity to assess its irradiation damage behavior in terms of its microstructure and mechanical property evolution. The results of room temperature compression testing show that AlNbMoZrB alloy has excellent mechanical property with compression yield strength ~1180 MPa, fracture strength ~1274 MPa, and plasticity ~4.8%. By comparatively examining the phase structure and microstructure evolution of AlNbMoZrB alloy before and after irradiation, it is found that AlNbMoZrB alloy has a typical dendrite structure, in which the dendrite region is a matrix phase with disordered BCC structure, and the interdendrite region is composed of FCC structure Al-Zr phase and α-Zr phase. After irradiation with Kr ions, the α-Zr phase underwent an amorphous transformation. At the same time, high density <100> and 1/2<111> dislocation loops are also generated. The volume density of the dislocation loop is ~4.11×10²² m^-3 and the size is between 12 nm and 16 nm after subjected Kr ions irradiation at room temperature. The volume density of the dislocation loop decreased to ~1.63×10²² m^-3 and the size increased to 23~27 nm after subjected the same Kr ions irradiation at 300℃.